4
\begin{eqnarray*} && -m_{2}\,g\left(y_{1}+r_{2}\,\sin({\theta_{2}})
5
\right) - m_{3}\,g\left(y_{2}+r_{3}\,\sin({\theta_{3}})\right) - m_{4}
6
\,g\left(y_{3}+r_{4}\,\sin({\theta_{4}})\right) - m_{5}\,g\left(y_{4}+
7
r_{5}\,\sin({\theta_{5}})\right) \\ &&\quad\mbox{} - m_{6}\,g\left(y_{
8
5}+r_{6}\,\sin({\theta_{6}})\right) - m_{7}\,g\left(y_{6}+r_{7}\,\sin(
9
{\theta_{7}})\right) - m_{8}\,g\left(y_{7}+r_{8}\,\sin({\theta_{8}})
10
\right) - m_{9}\,g\left(y_{8}+r_{9}\,\sin({\theta_{9}})\right)
11
\\ &&\quad\mbox{} - m_{10}\,g\left(y_{9}+r_{10}\,\sin({\theta_{10}})
12
\right) + \frac{m_{1}\left({r_{1}}^2\,{\sin({\theta_{1}})}^2\,{{
13
\dot{\theta}_{1}}}^2+{r_{1}}^2\,{\cos({\theta_{1}})}^2\,{{\dot{\theta}
14
_{1}}}^2\right)}{2} \\ &&\quad\mbox{} + \frac{J_{1}\,{{\dot{\theta}_{1
15
}}}^2}{2} + \frac{m_{2}\left(\left({\dot{x}_{1}}-r_{2}\,\sin({\theta_{
16
2}})\,{\dot{\theta}_{2}}\right)^2+\left({\dot{y}_{1}}+r_{2}\,\cos({
17
\theta_{2}})\,{\dot{\theta}_{2}}\right)^2\right)}{2} \\ &&\quad\mbox{}
18
+ \frac{J_{2}\,{{\dot{\theta}_{2}}}^2}{2} + \frac{m_{3}\left(\left({
19
\dot{x}_{2}}-r_{3}\,\sin({\theta_{3}})\,{\dot{\theta}_{3}}\right)^2+
20
\left({\dot{y}_{2}}+r_{3}\,\cos({\theta_{3}})\,{\dot{\theta}_{3}}
21
\right)^2\right)}{2} \\ &&\quad\mbox{} + \frac{J_{3}\,{{\dot{\theta}_{
22
3}}}^2}{2} + \frac{m_{4}\left(\left({\dot{x}_{3}}-r_{4}\,\sin({\theta
23
_{4}})\,{\dot{\theta}_{4}}\right)^2+\left({\dot{y}_{3}}+r_{4}\,\cos({
24
\theta_{4}})\,{\dot{\theta}_{4}}\right)^2\right)}{2} \\ &&\quad\mbox{}
25
+ \frac{J_{4}\,{{\dot{\theta}_{4}}}^2}{2} + \frac{m_{5}\left(\left({
26
\dot{x}_{4}}-r_{5}\,\sin({\theta_{5}})\,{\dot{\theta}_{5}}\right)^2+
27
\left({\dot{y}_{4}}+r_{5}\,\cos({\theta_{5}})\,{\dot{\theta}_{5}}
28
\right)^2\right)}{2} \\ &&\quad\mbox{} + \frac{J_{5}\,{{\dot{\theta}_{
29
5}}}^2}{2} + \frac{m_{6}\left(\left({\dot{x}_{5}}-r_{6}\,\sin({\theta
30
_{6}})\,{\dot{\theta}_{6}}\right)^2+\left({\dot{y}_{5}}+r_{6}\,\cos({
31
\theta_{6}})\,{\dot{\theta}_{6}}\right)^2\right)}{2} \\ &&\quad\mbox{}
32
+ \frac{J_{6}\,{{\dot{\theta}_{6}}}^2}{2} + \frac{m_{7}\left(\left({
33
\dot{x}_{6}}-r_{7}\,\sin({\theta_{7}})\,{\dot{\theta}_{7}}\right)^2+
34
\left({\dot{y}_{6}}+r_{7}\,\cos({\theta_{7}})\,{\dot{\theta}_{7}}
35
\right)^2\right)}{2} \\ &&\quad\mbox{} + \frac{J_{7}\,{{\dot{\theta}_{
36
7}}}^2}{2} + \frac{m_{8}\left(\left({\dot{x}_{7}}-r_{8}\,\sin({\theta
37
_{8}})\,{\dot{\theta}_{8}}\right)^2+\left({\dot{y}_{7}}+r_{8}\,\cos({
38
\theta_{8}})\,{\dot{\theta}_{8}}\right)^2\right)}{2} \\ &&\quad\mbox{}
39
+ \frac{J_{8}\,{{\dot{\theta}_{8}}}^2}{2} + \frac{m_{9}\left(\left({
40
\dot{x}_{8}}-r_{9}\,\sin({\theta_{9}})\,{\dot{\theta}_{9}}\right)^2+
41
\left({\dot{y}_{8}}+r_{9}\,\cos({\theta_{9}})\,{\dot{\theta}_{9}}
42
\right)^2\right)}{2} \\ &&\quad\mbox{} + \frac{J_{9}\,{{\dot{\theta}_{
43
9}}}^2}{2} \\ &&\quad\mbox{} + \frac{m_{10}\left(\left({\dot{x}_{9}}-r
44
_{10}\,\sin({\theta_{10}})\,{\dot{\theta}_{10}}\right)^2+\left({
45
\dot{y}_{9}}+r_{10}\,\cos({\theta_{10}})\,{\dot{\theta}_{10}}\right)^2
46
\right)}{2} \\ &&\quad\mbox{} + \frac{J_{10}\,{{\dot{\theta}_{10}}}^2
47
}{2} - m_{1}\,g\,r_{1}\,\sin({\theta_{1}}) \end{eqnarray*}
48
Lhs of Euler Equations
50
\[ LL(x_{7}) = m_{8}\,{\ddot{x}_{7}} - m_{8}\,r_{8}\,\cos({\theta_{8}}
51
)\,{{\dot{\theta}_{8}}}^2 - m_{8}\,r_{8}\,\sin({\theta_{8}})\,{
53
\[ LL(y_{3}) = m_{4}\,{\ddot{y}_{3}} - m_{4}\,r_{4}\,\sin({\theta_{4}}
54
)\,{{\dot{\theta}_{4}}}^2 + m_{4}\,r_{4}\,\cos({\theta_{4}})\,{
55
\ddot{\theta}_{4}} + m_{4}\,g \]
56
\[ LL(y_{5}) = m_{6}\,{\ddot{y}_{5}} - m_{6}\,r_{6}\,\sin({\theta_{6}}
57
)\,{{\dot{\theta}_{6}}}^2 + m_{6}\,r_{6}\,\cos({\theta_{6}})\,{
58
\ddot{\theta}_{6}} + m_{6}\,g \]
59
\[ LL({\theta_{1}}) = m_{1}\,{r_{1}}^2\,{\ddot{\theta}_{1}} + J_{1}\,{
60
\ddot{\theta}_{1}} + m_{1}\,g\,r_{1}\,\cos({\theta_{1}}) \]
61
\[ LL(x_{8}) = m_{9}\,{\ddot{x}_{8}} - m_{9}\,r_{9}\,\cos({\theta_{9}}
62
)\,{{\dot{\theta}_{9}}}^2 - m_{9}\,r_{9}\,\sin({\theta_{9}})\,{
64
\[ LL(y_{4}) = m_{5}\,{\ddot{y}_{4}} - m_{5}\,r_{5}\,\sin({\theta_{5}}
65
)\,{{\dot{\theta}_{5}}}^2 + m_{5}\,r_{5}\,\cos({\theta_{5}})\,{
66
\ddot{\theta}_{5}} + m_{5}\,g \]
67
\begin{eqnarray*} LL({\theta_{9}}) &=& -m_{9}\,r_{9}\,\sin({\theta_{9}
68
})\,{\ddot{x}_{8}} + m_{9}\,{r_{9}}^2\,{\ddot{\theta}_{9}} + m_{9}\,r
69
_{9}\,\cos({\theta_{9}})\,{\ddot{y}_{8}} + J_{9}\,{\ddot{\theta}_{9}}
70
\\ &&\quad\mbox{} + m_{9}\,g\,r_{9}\,\cos({\theta_{9}})
72
\begin{eqnarray*} LL({\theta_{2}}) &=& -m_{2}\,r_{2}\,\sin({\theta_{2}
73
})\,{\ddot{x}_{1}} + m_{2}\,{r_{2}}^2\,{\ddot{\theta}_{2}} + m_{2}\,r
74
_{2}\,\cos({\theta_{2}})\,{\ddot{y}_{1}} + J_{2}\,{\ddot{\theta}_{2}}
75
\\ &&\quad\mbox{} + m_{2}\,g\,r_{2}\,\cos({\theta_{2}})
77
\[ LL(x_{9}) = m_{10}\,{\ddot{x}_{9}} - m_{10}\,r_{10}\,\cos({\theta_{
78
10}})\,{{\dot{\theta}_{10}}}^2 - m_{10}\,r_{10}\,\sin({\theta_{10}})\,
79
{\ddot{\theta}_{10}} \]
80
\begin{eqnarray*} LL({\theta_{4}}) &=& -m_{4}\,r_{4}\,\sin({\theta_{4}
81
})\,{\ddot{x}_{3}} + m_{4}\,{r_{4}}^2\,{\ddot{\theta}_{4}} + m_{4}\,r
82
_{4}\,\cos({\theta_{4}})\,{\ddot{y}_{3}} + J_{4}\,{\ddot{\theta}_{4}}
83
\\ &&\quad\mbox{} + m_{4}\,g\,r_{4}\,\cos({\theta_{4}})
85
\begin{eqnarray*} LL({\theta_{10}}) &=& -m_{10}\,r_{10}\,\sin({\theta
86
_{10}})\,{\ddot{x}_{9}} + m_{10}\,{r_{10}}^2\,{\ddot{\theta}_{10}} + m
87
_{10}\,r_{10}\,\cos({\theta_{10}})\,{\ddot{y}_{9}} + J_{10}\,{
88
\ddot{\theta}_{10}} \\ &&\quad\mbox{} + m_{10}\,g\,r_{10}\,\cos({
89
\theta_{10}}) \end{eqnarray*}
90
\[ LL(y_{7}) = m_{8}\,{\ddot{y}_{7}} - m_{8}\,r_{8}\,\sin({\theta_{8}}
91
)\,{{\dot{\theta}_{8}}}^2 + m_{8}\,r_{8}\,\cos({\theta_{8}})\,{
92
\ddot{\theta}_{8}} + m_{8}\,g \]
93
\begin{eqnarray*} LL({\theta_{3}}) &=& -m_{3}\,r_{3}\,\sin({\theta_{3}
94
})\,{\ddot{x}_{2}} + m_{3}\,{r_{3}}^2\,{\ddot{\theta}_{3}} + m_{3}\,r
95
_{3}\,\cos({\theta_{3}})\,{\ddot{y}_{2}} + J_{3}\,{\ddot{\theta}_{3}}
96
\\ &&\quad\mbox{} + m_{3}\,g\,r_{3}\,\cos({\theta_{3}})
98
\[ LL(y_{6}) = m_{7}\,{\ddot{y}_{6}} - m_{7}\,r_{7}\,\sin({\theta_{7}}
99
)\,{{\dot{\theta}_{7}}}^2 + m_{7}\,r_{7}\,\cos({\theta_{7}})\,{
100
\ddot{\theta}_{7}} + m_{7}\,g \]
101
\begin{eqnarray*} LL({\theta_{5}}) &=& -m_{5}\,r_{5}\,\sin({\theta_{5}
102
})\,{\ddot{x}_{4}} + m_{5}\,{r_{5}}^2\,{\ddot{\theta}_{5}} + m_{5}\,r
103
_{5}\,\cos({\theta_{5}})\,{\ddot{y}_{4}} + J_{5}\,{\ddot{\theta}_{5}}
104
\\ &&\quad\mbox{} + m_{5}\,g\,r_{5}\,\cos({\theta_{5}})
106
\[ LL(x_{2}) = m_{3}\,{\ddot{x}_{2}} - m_{3}\,r_{3}\,\cos({\theta_{3}}
107
)\,{{\dot{\theta}_{3}}}^2 - m_{3}\,r_{3}\,\sin({\theta_{3}})\,{
108
\ddot{\theta}_{3}} \]
109
\[ LL(y_{8}) = m_{9}\,{\ddot{y}_{8}} - m_{9}\,r_{9}\,\sin({\theta_{9}}
110
)\,{{\dot{\theta}_{9}}}^2 + m_{9}\,r_{9}\,\cos({\theta_{9}})\,{
111
\ddot{\theta}_{9}} + m_{9}\,g \]
112
\begin{eqnarray*} LL({\theta_{6}}) &=& -m_{6}\,r_{6}\,\sin({\theta_{6}
113
})\,{\ddot{x}_{5}} + m_{6}\,{r_{6}}^2\,{\ddot{\theta}_{6}} + m_{6}\,r
114
_{6}\,\cos({\theta_{6}})\,{\ddot{y}_{5}} + J_{6}\,{\ddot{\theta}_{6}}
115
\\ &&\quad\mbox{} + m_{6}\,g\,r_{6}\,\cos({\theta_{6}})
118
\[ LL(x_{3}) = m_{4}\,{\ddot{x}_{3}} - m_{4}\,r_{4}\,\cos({\theta_{4}}
119
)\,{{\dot{\theta}_{4}}}^2 - m_{4}\,r_{4}\,\sin({\theta_{4}})\,{
120
\ddot{\theta}_{4}} \]
121
\[ LL(x_{5}) = m_{6}\,{\ddot{x}_{5}} - m_{6}\,r_{6}\,\cos({\theta_{6}}
122
)\,{{\dot{\theta}_{6}}}^2 - m_{6}\,r_{6}\,\sin({\theta_{6}})\,{
123
\ddot{\theta}_{6}} \]
124
\[ LL(y_{1}) = m_{2}\,{\ddot{y}_{1}} - m_{2}\,r_{2}\,\sin({\theta_{2}}
125
)\,{{\dot{\theta}_{2}}}^2 + m_{2}\,r_{2}\,\cos({\theta_{2}})\,{
126
\ddot{\theta}_{2}} + m_{2}\,g \]
127
\[ LL(x_{1}) = m_{2}\,{\ddot{x}_{1}} - m_{2}\,r_{2}\,\cos({\theta_{2}}
128
)\,{{\dot{\theta}_{2}}}^2 - m_{2}\,r_{2}\,\sin({\theta_{2}})\,{
129
\ddot{\theta}_{2}} \]
130
\begin{eqnarray*} LL({\theta_{7}}) &=& -m_{7}\,r_{7}\,\sin({\theta_{7}
131
})\,{\ddot{x}_{6}} + m_{7}\,{r_{7}}^2\,{\ddot{\theta}_{7}} + m_{7}\,r
132
_{7}\,\cos({\theta_{7}})\,{\ddot{y}_{6}} + J_{7}\,{\ddot{\theta}_{7}}
133
\\ &&\quad\mbox{} + m_{7}\,g\,r_{7}\,\cos({\theta_{7}})
135
\[ LL(x_{4}) = m_{5}\,{\ddot{x}_{4}} - m_{5}\,r_{5}\,\cos({\theta_{5}}
136
)\,{{\dot{\theta}_{5}}}^2 - m_{5}\,r_{5}\,\sin({\theta_{5}})\,{
137
\ddot{\theta}_{5}} \]
138
\[ LL(y_{9}) = m_{10}\,{\ddot{y}_{9}} - m_{10}\,r_{10}\,\sin({\theta_{
139
10}})\,{{\dot{\theta}_{10}}}^2 + m_{10}\,r_{10}\,\cos({\theta_{10}})\,
140
{\ddot{\theta}_{10}} + m_{10}\,g \]
141
\[ LL(x_{6}) = m_{7}\,{\ddot{x}_{6}} - m_{7}\,r_{7}\,\cos({\theta_{7}}
142
)\,{{\dot{\theta}_{7}}}^2 - m_{7}\,r_{7}\,\sin({\theta_{7}})\,{
143
\ddot{\theta}_{7}} \]
144
\[ LL(y_{2}) = m_{3}\,{\ddot{y}_{2}} - m_{3}\,r_{3}\,\sin({\theta_{3}}
145
)\,{{\dot{\theta}_{3}}}^2 + m_{3}\,r_{3}\,\cos({\theta_{3}})\,{
146
\ddot{\theta}_{3}} + m_{3}\,g \]
147
\begin{eqnarray*} LL({\theta_{8}}) &=& -m_{8}\,r_{8}\,\sin({\theta_{8}
148
})\,{\ddot{x}_{7}} + m_{8}\,{r_{8}}^2\,{\ddot{\theta}_{8}} + m_{8}\,r
149
_{8}\,\cos({\theta_{8}})\,{\ddot{y}_{7}} + J_{8}\,{\ddot{\theta}_{8}}
150
\\ &&\quad\mbox{} + m_{8}\,g\,r_{8}\,\cos({\theta_{8}})
153
$mrc_k=m_k r_k \cos(\theta_k)$
154
$mrs_k=m_k r_k \sin(\theta_k)$
155
$M(q)\ddot{q}+C(q)\dot{q}^2 +R(q,\dot{q})$,M:
157
$$ \left( \begin{array}{cccccccccccccccccccccccccccccc} m_{2} & 0 & 0
158
& 0 & 0 & -mrs_{2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 &
159
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & m_{2} & 0 & 0 &
160
0 & mrc_{2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 &
161
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & m_{1}\,{r_{1}}^2+J_{
162
1} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
163
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & m_{3} & 0 & 0
164
& 0 & 0 & -mrs_{3} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 &
165
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & m_{3} & 0 & 0 &
166
0 & mrc_{3} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 &
167
0 & 0 & 0 & 0 & 0 & 0 & 0 \cr -mrs_{2} & mrc_{2} & 0 & 0 & 0 & m_{2}\,
168
{r_{2}}^2+J_{2} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 &
169
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 &
170
m_{4} & 0 & 0 & 0 & 0 & -mrs_{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
171
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & m
172
_{4} & 0 & 0 & 0 & mrc_{4} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
173
& 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & -mrs_{3} & mrc_{3} & 0 &
174
0 & 0 & m_{3}\,{r_{3}}^2+J_{3} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
175
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0
176
& 0 & 0 & 0 & m_{5} & 0 & 0 & 0 & 0 & -mrs_{5} & 0 & 0 & 0 & 0 & 0 &
177
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 &
178
0 & 0 & 0 & m_{5} & 0 & 0 & 0 & mrc_{5} & 0 & 0 & 0 & 0 & 0 & 0 & 0 &
179
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & -mrs_{4} &
180
mrc_{4} & 0 & 0 & 0 & m_{4}\,{r_{4}}^2+J_{4} & 0 & 0 & 0 & 0 & 0 & 0
181
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0
182
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & m_{6} & 0 & 0 & 0 & 0 & -mrs_{6} & 0 &
183
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 &
184
0 & 0 & 0 & 0 & 0 & 0 & 0 & m_{6} & 0 & 0 & 0 & mrc_{6} & 0 & 0 & 0 &
185
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 &
186
0 & -mrs_{5} & mrc_{5} & 0 & 0 & 0 & m_{5}\,{r_{5}}^2+J_{5} & 0 & 0 &
187
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 &
188
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & m_{7} & 0 & 0 & 0 & 0 & -
189
mrs_{7} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0
190
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & m_{7} & 0 & 0 & 0 & mrc_{7}
191
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
192
& 0 & 0 & 0 & 0 & -mrs_{6} & mrc_{6} & 0 & 0 & 0 & m_{6}\,{r_{6}}^2+J
193
_{6} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0
194
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & m_{8} & 0
195
& 0 & 0 & 0 & -mrs_{8} & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0
196
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & m_{8} & 0
197
& 0 & 0 & mrc_{8} & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0
198
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -mrs_{7} & mrc_{7} & 0 & 0 & 0
199
& m_{7}\,{r_{7}}^2+J_{7} & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 &
200
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
201
& 0 & 0 & m_{9} & 0 & 0 & 0 & 0 & -mrs_{9} & 0 & 0 & 0 \cr 0 & 0 & 0
202
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
203
& 0 & 0 & m_{9} & 0 & 0 & 0 & mrc_{9} & 0 & 0 & 0 \cr 0 & 0 & 0 & 0
204
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -mrs_{8} &
205
mrc_{8} & 0 & 0 & 0 & m_{8}\,{r_{8}}^2+J_{8} & 0 & 0 & 0 & 0 & 0 & 0
206
\cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
207
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & m_{10} & 0 & 0 & 0 & 0 & -mrs_{10} \cr
208
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
209
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & m_{10} & 0 & 0 & 0 & mrc_{10} \cr 0 & 0
210
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
211
& 0 & 0 & -mrs_{9} & mrc_{9} & 0 & 0 & 0 & m_{9}\,{r_{9}}^2+J_{9} & 0
212
& 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
213
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0
214
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
215
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0
216
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
217
& 0 & -mrs_{10} & mrc_{10} & 0 & 0 & 0 & m_{10}\,{r_{10}}^2+J_{10}
218
\end{array} \right) $$
221
$$ \left( \begin{array}{cccccccccccccccccccccccccccccc} 0 & 0 & 0 & 0
222
& 0 & -m_{2}\,r_{2}\,\cos({\theta_{2}}) & 0 & 0 & 0 & 0 & 0 & 0 & 0
223
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
224
\cr 0 & 0 & 0 & 0 & 0 & -m_{2}\,r_{2}\,\sin({\theta_{2}}) & 0 & 0 & 0
225
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
226
& 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
227
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
228
\cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -m_{3}\,r_{3}\,\cos({\theta_{3}})
229
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
230
& 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -m_{3}\,r_{3}\,
231
\sin({\theta_{3}}) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
232
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
233
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
234
& 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -m_{4
235
}\,r_{4}\,\cos({\theta_{4}}) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
236
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
237
& 0 & 0 & -m_{4}\,r_{4}\,\sin({\theta_{4}}) & 0 & 0 & 0 & 0 & 0 & 0
238
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0
239
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
240
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
241
& 0 & 0 & 0 & 0 & 0 & -m_{5}\,r_{5}\,\cos({\theta_{5}}) & 0 & 0 & 0
242
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0
243
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -m_{5}\,r_{5}\,\sin({\theta_{5}
244
}) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0
245
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
246
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0
247
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -m_{6}\,r_{6}\,\cos
248
({\theta_{6}}) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0
249
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -m
250
_{6}\,r_{6}\,\sin({\theta_{6}}) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 &
251
0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 &
252
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 &
253
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
254
& 0 & -m_{7}\,r_{7}\,\cos({\theta_{7}}) & 0 & 0 & 0 & 0 & 0 & 0 & 0
255
& 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
256
& 0 & 0 & 0 & 0 & 0 & -m_{7}\,r_{7}\,\sin({\theta_{7}}) & 0 & 0 & 0
257
& 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
258
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
259
& 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
260
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -m_{8}\,r_{8}\,\cos({\theta_{8}})
261
& 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
262
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -m_{8}\,r_{8}\,\sin
263
({\theta_{8}}) & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0
264
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
265
& 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
266
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -m_{9}
267
\,r_{9}\,\cos({\theta_{9}}) & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0
268
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
269
& 0 & 0 & -m_{9}\,r_{9}\,\sin({\theta_{9}}) & 0 & 0 & 0 \cr 0 & 0 & 0
270
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
271
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0
272
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
273
& 0 & 0 & 0 & 0 & 0 & -m_{10}\,r_{10}\,\cos({\theta_{10}}) \cr 0 & 0
274
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
275
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -m_{10}\,r_{10}\,\sin({
276
\theta_{10}}) \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 &
277
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr
278
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
279
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0
280
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
281
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
282
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
283
& 0 & 0 & 0 & 0 \end{array} \right) $$
286
$$ \left( \begin{array}{c} 0 \cr m_{2}\,g \cr m_{1}\,g\,r_{1}\,\cos({
287
\theta_{1}}) \cr 0 \cr m_{3}\,g \cr m_{2}\,g\,r_{2}\,\cos({\theta_{2}}
288
) \cr 0 \cr m_{4}\,g \cr m_{3}\,g\,r_{3}\,\cos({\theta_{3}}) \cr 0
289
\cr m_{5}\,g \cr m_{4}\,g\,r_{4}\,\cos({\theta_{4}}) \cr 0 \cr m_{6}
290
\,g \cr m_{5}\,g\,r_{5}\,\cos({\theta_{5}}) \cr 0 \cr m_{7}\,g \cr m_{
291
6}\,g\,r_{6}\,\cos({\theta_{6}}) \cr 0 \cr m_{8}\,g \cr m_{7}\,g\,r_{7
292
}\,\cos({\theta_{7}}) \cr 0 \cr m_{9}\,g \cr m_{8}\,g\,r_{8}\,\cos({
293
\theta_{8}}) \cr 0 \cr m_{10}\,g \cr m_{9}\,g\,r_{9}\,\cos({\theta_{9}
294
}) \cr 0 \cr 0 \cr m_{10}\,g\,r_{10}\,\cos({\theta_{10}})
295
\end{array} \right) $$
298
\[ x_{1} - 2\,r_{1}\,\cos({\theta_{1}}) \]
299
\[ y_{1} - 2\,r_{1}\,\sin({\theta_{1}}) \]
300
\[ x_{2} - x_{1} - 2\,r_{2}\,\cos({\theta_{2}}) \]
301
\[ y_{2} - y_{1} - 2\,r_{2}\,\sin({\theta_{2}}) \]
302
\[ x_{3} - x_{2} - 2\,r_{3}\,\cos({\theta_{3}}) \]
303
\[ y_{3} - y_{2} - 2\,r_{3}\,\sin({\theta_{3}}) \]
304
\[ x_{4} - x_{3} - 2\,r_{4}\,\cos({\theta_{4}}) \]
305
\[ y_{4} - y_{3} - 2\,r_{4}\,\sin({\theta_{4}}) \]
306
\[ x_{5} - x_{4} - 2\,r_{5}\,\cos({\theta_{5}}) \]
307
\[ y_{5} - y_{4} - 2\,r_{5}\,\sin({\theta_{5}}) \]
308
\[ x_{6} - x_{5} - 2\,r_{6}\,\cos({\theta_{6}}) \]
309
\[ y_{6} - y_{5} - 2\,r_{6}\,\sin({\theta_{6}}) \]
310
\[ x_{7} - x_{6} - 2\,r_{7}\,\cos({\theta_{7}}) \]
311
\[ y_{7} - y_{6} - 2\,r_{7}\,\sin({\theta_{7}}) \]
312
\[ x_{8} - x_{7} - 2\,r_{8}\,\cos({\theta_{8}}) \]
313
\[ y_{8} - y_{7} - 2\,r_{8}\,\sin({\theta_{8}}) \]
314
\[ x_{9} - x_{8} - 2\,r_{9}\,\cos({\theta_{9}}) \]
315
\[ y_{9} - y_{8} - 2\,r_{9}\,\sin({\theta_{9}}) \]
316
\[ x_{10} - x_{9} - 2\,r_{10}\,\cos({\theta_{10}}) \]
317
\[ y_{10} - y_{9} - 2\,r_{10}\,\sin({\theta_{10}}) \]
318
Time derivative of constraints : $A'(q)\dot{q}$
320
$$ \left( \begin{array}{cccccccccccccccccccccccccccccc} 1 & 0 & 2\,r_{
321
1}\,\sin({\theta_{1}}) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
322
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 1
323
& -2\,r_{1}\,\cos({\theta_{1}}) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
324
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
325
& 0 \cr -1 & 0 & 0 & 1 & 0 & 2\,r_{2}\,\sin({\theta_{2}}) & 0 & 0 & 0
326
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
327
& 0 & 0 & 0 & 0 \cr 0 & -1 & 0 & 0 & 1 & -2\,r_{2}\,\cos({\theta_{2}}
328
) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
329
& 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 2\,r
330
_{3}\,\sin({\theta_{3}}) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
331
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & -1 & 0 &
332
0 & 1 & -2\,r_{3}\,\cos({\theta_{3}}) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
333
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0
334
& 0 & 0 & -1 & 0 & 0 & 1 & 0 & 2\,r_{4}\,\sin({\theta_{4}}) & 0 & 0
335
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0
336
& 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & -2\,r_{4}\,\cos({\theta_{4
337
}}) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 &
338
0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 2\,
339
r_{5}\,\sin({\theta_{5}}) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
340
& 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 &
341
0 & 1 & -2\,r_{5}\,\cos({\theta_{5}}) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
342
& 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
343
& 0 & 0 & -1 & 0 & 0 & 1 & 0 & 2\,r_{6}\,\sin({\theta_{6}}) & 0 & 0
344
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0
345
& 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & -2\,r_{6}\,\cos({\theta_{6
346
}}) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0
347
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 2
348
\,r_{7}\,\sin({\theta_{7}}) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0
349
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0
350
& 0 & 1 & -2\,r_{7}\,\cos({\theta_{7}}) & 0 & 0 & 0 & 0 & 0 & 0 & 0
351
& 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
352
& 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 2\,r_{8}\,\sin({\theta_{8}}) & 0
353
& 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
354
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & -2\,r_{8}\,\cos({
355
\theta_{8}}) & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
356
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1
357
& 0 & 2\,r_{9}\,\sin({\theta_{9}}) & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0
358
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
359
& -1 & 0 & 0 & 1 & -2\,r_{9}\,\cos({\theta_{9}}) & 0 & 0 & 0 \cr 0 &
360
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
361
& 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & 0 & 2\,r_{10}\,\sin({\theta_{
362
10}}) \cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 &
363
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 0 & 0 & 1 & -2\,r_{10}\,
364
\cos({\theta_{10}}) \end{array} \right) $$
367
\begin{eqnarray*} && \frac{m_{1}\left({r_{1}}^2\,{\sin({\theta_{1}})}^
368
2\,{{\dot{\theta}_{1}}}^2+{r_{1}}^2\,{\cos({\theta_{1}})}^2\,{{
369
\dot{\theta}_{1}}}^2\right)}{2} + \frac{J_{1}\,{{\dot{\theta}_{1}}}^2
370
}{2} + \frac{J_{2}\,{{\dot{\theta}_{2}}}^2}{2} \\ &&\quad\mbox{} +
371
\frac{J_{3}\,{{\dot{\theta}_{3}}}^2}{2} + \frac{J_{4}\,{{\dot{\theta}
372
_{4}}}^2}{2} + \frac{J_{5}\,{{\dot{\theta}_{5}}}^2}{2} + \frac{J_{6}\,
373
{{\dot{\theta}_{6}}}^2}{2} + \frac{J_{7}\,{{\dot{\theta}_{7}}}^2}{2}
374
+ \frac{J_{8}\,{{\dot{\theta}_{8}}}^2}{2} \\ &&\quad\mbox{} + \frac{J
375
_{9}\,{{\dot{\theta}_{9}}}^2}{2} + \frac{J_{10}\,{{\dot{\theta}_{10}}}
376
^2}{2} + m_{1}\,g\,r_{1}\,\sin({\theta_{1}}) \\ &&\quad\mbox{} +
377
\frac{m_{2}\left(\left(-2\,r_{1}\,\sin({\theta_{1}})\,{\dot{\theta}_{1
378
}}-r_{2}\,\sin({\theta_{2}})\,{\dot{\theta}_{2}}\right)^2+\left(2\,r_{
379
1}\,\cos({\theta_{1}})\,{\dot{\theta}_{1}}+r_{2}\,\cos({\theta_{2}})\,
380
{\dot{\theta}_{2}}\right)^2\right)}{2} \\ &&\quad\mbox{} + \frac{m_{3}
381
\left(\left(-2\,r_{1}\,\sin({\theta_{1}})\,{\dot{\theta}_{1}}-2\,r_{2}
382
\,\sin({\theta_{2}})\,{\dot{\theta}_{2}}-r_{3}\,\sin({\theta_{3}})\,{
383
\dot{\theta}_{3}}\right)^2+\left(2\,r_{1}\,\cos({\theta_{1}})\,{
384
\dot{\theta}_{1}}+2\,r_{2}\,\cos({\theta_{2}})\,{\dot{\theta}_{2}}+r_{
385
3}\,\cos({\theta_{3}})\,{\dot{\theta}_{3}}\right)^2\right)}{2}
386
\\ &&\quad\mbox{} + \frac{m_{4}\left(\left(-2\,r_{3}\,\sin({\theta_{3
387
}})\,{\dot{\theta}_{3}}-2\,r_{1}\,\sin({\theta_{1}})\,{\dot{\theta}_{1
388
}}-2\,r_{2}\,\sin({\theta_{2}})\,{\dot{\theta}_{2}}-r_{4}\,\sin({
389
\theta_{4}})\,{\dot{\theta}_{4}}\right)^2+\left(2\,r_{3}\,\cos({\theta
390
_{3}})\,{\dot{\theta}_{3}}+2\,r_{1}\,\cos({\theta_{1}})\,{\dot{\theta}
391
_{1}}+2\,r_{2}\,\cos({\theta_{2}})\,{\dot{\theta}_{2}}+r_{4}\,\cos({
392
\theta_{4}})\,{\dot{\theta}_{4}}\right)^2\right)}{2} \\ &&\quad\mbox{}
393
+ \frac{m_{5}\left(\left(-2\,r_{1}\,\sin({\theta_{1}})\,{\dot{\theta}
394
_{1}}-2\,r_{3}\,\sin({\theta_{3}})\,{\dot{\theta}_{3}}-2\,r_{2}\,\sin(
395
{\theta_{2}})\,{\dot{\theta}_{2}}-2\,r_{4}\,\sin({\theta_{4}})\,{
396
\dot{\theta}_{4}}-r_{5}\,\sin({\theta_{5}})\,{\dot{\theta}_{5}}\right)
397
^2+\left(2\,r_{3}\,\cos({\theta_{3}})\,{\dot{\theta}_{3}}+2\,r_{4}\,
398
\cos({\theta_{4}})\,{\dot{\theta}_{4}}+2\,r_{1}\,\cos({\theta_{1}})\,{
399
\dot{\theta}_{1}}+2\,r_{2}\,\cos({\theta_{2}})\,{\dot{\theta}_{2}}+r_{
400
5}\,\cos({\theta_{5}})\,{\dot{\theta}_{5}}\right)^2\right)}{2}
401
\\ &&\quad\mbox{} + m_{6}\,g\left(2\,r_{1}\,\sin({\theta_{1}})+2\,r_{
402
5}\,\sin({\theta_{5}})+2\,r_{3}\,\sin({\theta_{3}})+2\,r_{2}\,\sin({
403
\theta_{2}})+2\,r_{4}\,\sin({\theta_{4}})+r_{6}\,\sin({\theta_{6}})
404
\right) \\ &&\quad\mbox{} + m_{8}\,g\left(2\,r_{7}\,\sin({\theta_{7}})
405
+2\,r_{1}\,\sin({\theta_{1}})+2\,r_{6}\,\sin({\theta_{6}})+2\,r_{5}\,
406
\sin({\theta_{5}})+2\,r_{3}\,\sin({\theta_{3}})+2\,r_{2}\,\sin({\theta
407
_{2}})+2\,r_{4}\,\sin({\theta_{4}})+r_{8}\,\sin({\theta_{8}})\right)
408
\\ &&\quad\mbox{} + m_{9}\,g\left(2\,r_{7}\,\sin({\theta_{7}})+2\,r_{
409
8}\,\sin({\theta_{8}})+2\,r_{1}\,\sin({\theta_{1}})+2\,r_{6}\,\sin({
410
\theta_{6}})+2\,r_{5}\,\sin({\theta_{5}})+2\,r_{3}\,\sin({\theta_{3}})
411
+2\,r_{2}\,\sin({\theta_{2}})+2\,r_{4}\,\sin({\theta_{4}})+r_{9}\,\sin
412
({\theta_{9}})\right) \\ &&\quad\mbox{} + m_{10}\,g\left(2\,r_{7}\,
413
\sin({\theta_{7}})+2\,r_{9}\,\sin({\theta_{9}})+2\,r_{8}\,\sin({\theta
414
_{8}})+2\,r_{1}\,\sin({\theta_{1}})+2\,r_{6}\,\sin({\theta_{6}})+2\,r
415
_{5}\,\sin({\theta_{5}})+2\,r_{3}\,\sin({\theta_{3}})+2\,r_{2}\,\sin({
416
\theta_{2}})+2\,r_{4}\,\sin({\theta_{4}})+r_{10}\,\sin({\theta_{10}})
417
\right) \\ &&\quad\mbox{} + m_{7}\,g\left(2\,r_{1}\,\sin({\theta_{1}})
418
+2\,r_{6}\,\sin({\theta_{6}})+2\,r_{5}\,\sin({\theta_{5}})+2\,r_{3}\,
419
\sin({\theta_{3}})+2\,r_{2}\,\sin({\theta_{2}})+2\,r_{4}\,\sin({\theta
420
_{4}})+r_{7}\,\sin({\theta_{7}})\right) \\ &&\quad\mbox{} + m_{3}\,g
421
\left(2\,r_{1}\,\sin({\theta_{1}})+2\,r_{2}\,\sin({\theta_{2}})+r_{3}
422
\,\sin({\theta_{3}})\right) \\ &&\quad\mbox{} + m_{4}\,g\left(2\,r_{3}
423
\,\sin({\theta_{3}})+2\,r_{1}\,\sin({\theta_{1}})+2\,r_{2}\,\sin({
424
\theta_{2}})+r_{4}\,\sin({\theta_{4}})\right) \\ &&\quad\mbox{} + m_{5
425
}\,g\left(2\,r_{1}\,\sin({\theta_{1}})+2\,r_{3}\,\sin({\theta_{3}})+2
426
\,r_{2}\,\sin({\theta_{2}})+2\,r_{4}\,\sin({\theta_{4}})+r_{5}\,\sin({
427
\theta_{5}})\right) \\ &&\quad\mbox{} + m_{2}\,g\left(2\,r_{1}\,\sin({
428
\theta_{1}})+r_{2}\,\sin({\theta_{2}})\right) \\ &&\quad\mbox{} +
429
\frac{m_{10}\left(\left(-2\,r_{7}\,\sin({\theta_{7}})\,{\dot{\theta}_{
430
7}}-2\,r_{9}\,\sin({\theta_{9}})\,{\dot{\theta}_{9}}-2\,r_{8}\,\sin({
431
\theta_{8}})\,{\dot{\theta}_{8}}-2\,r_{1}\,\sin({\theta_{1}})\,{
432
\dot{\theta}_{1}}-2\,r_{6}\,\sin({\theta_{6}})\,{\dot{\theta}_{6}}-2\,
433
r_{5}\,\sin({\theta_{5}})\,{\dot{\theta}_{5}}-2\,r_{3}\,\sin({\theta_{
434
3}})\,{\dot{\theta}_{3}}-2\,r_{2}\,\sin({\theta_{2}})\,{\dot{\theta}_{
435
2}}-2\,r_{4}\,\sin({\theta_{4}})\,{\dot{\theta}_{4}}-r_{10}\,\sin({
436
\theta_{10}})\,{\dot{\theta}_{10}}\right)^2+\left(2\,r_{7}\,\cos({
437
\theta_{7}})\,{\dot{\theta}_{7}}+2\,r_{9}\,\cos({\theta_{9}})\,{
438
\dot{\theta}_{9}}+2\,r_{8}\,\cos({\theta_{8}})\,{\dot{\theta}_{8}}+2\,
439
r_{1}\,\cos({\theta_{1}})\,{\dot{\theta}_{1}}+2\,r_{6}\,\cos({\theta_{
440
6}})\,{\dot{\theta}_{6}}+2\,r_{3}\,\cos({\theta_{3}})\,{\dot{\theta}_{
441
3}}+2\,r_{4}\,\cos({\theta_{4}})\,{\dot{\theta}_{4}}+2\,r_{2}\,\cos({
442
\theta_{2}})\,{\dot{\theta}_{2}}+2\,r_{5}\,\cos({\theta_{5}})\,{
443
\dot{\theta}_{5}}+r_{10}\,\cos({\theta_{10}})\,{\dot{\theta}_{10}}
444
\right)^2\right)}{2} \\ &&\quad\mbox{} + \frac{m_{7}\left(\left(-2\,r
445
_{1}\,\sin({\theta_{1}})\,{\dot{\theta}_{1}}-2\,r_{6}\,\sin({\theta_{6
446
}})\,{\dot{\theta}_{6}}-2\,r_{5}\,\sin({\theta_{5}})\,{\dot{\theta}_{5
447
}}-2\,r_{3}\,\sin({\theta_{3}})\,{\dot{\theta}_{3}}-2\,r_{2}\,\sin({
448
\theta_{2}})\,{\dot{\theta}_{2}}-2\,r_{4}\,\sin({\theta_{4}})\,{
449
\dot{\theta}_{4}}-r_{7}\,\sin({\theta_{7}})\,{\dot{\theta}_{7}}\right)
450
^2+\left(2\,r_{1}\,\cos({\theta_{1}})\,{\dot{\theta}_{1}}+2\,r_{6}\,
451
\cos({\theta_{6}})\,{\dot{\theta}_{6}}+2\,r_{3}\,\cos({\theta_{3}})\,{
452
\dot{\theta}_{3}}+2\,r_{4}\,\cos({\theta_{4}})\,{\dot{\theta}_{4}}+2\,
453
r_{2}\,\cos({\theta_{2}})\,{\dot{\theta}_{2}}+2\,r_{5}\,\cos({\theta_{
454
5}})\,{\dot{\theta}_{5}}+r_{7}\,\cos({\theta_{7}})\,{\dot{\theta}_{7}}
455
\right)^2\right)}{2} \\ &&\quad\mbox{} + \frac{m_{8}\left(\left(-2\,r
456
_{7}\,\sin({\theta_{7}})\,{\dot{\theta}_{7}}-2\,r_{1}\,\sin({\theta_{1
457
}})\,{\dot{\theta}_{1}}-2\,r_{6}\,\sin({\theta_{6}})\,{\dot{\theta}_{6
458
}}-2\,r_{5}\,\sin({\theta_{5}})\,{\dot{\theta}_{5}}-2\,r_{3}\,\sin({
459
\theta_{3}})\,{\dot{\theta}_{3}}-2\,r_{2}\,\sin({\theta_{2}})\,{
460
\dot{\theta}_{2}}-2\,r_{4}\,\sin({\theta_{4}})\,{\dot{\theta}_{4}}-r_{
461
8}\,\sin({\theta_{8}})\,{\dot{\theta}_{8}}\right)^2+\left(2\,r_{7}\,
462
\cos({\theta_{7}})\,{\dot{\theta}_{7}}+2\,r_{1}\,\cos({\theta_{1}})\,{
463
\dot{\theta}_{1}}+2\,r_{6}\,\cos({\theta_{6}})\,{\dot{\theta}_{6}}+2\,
464
r_{3}\,\cos({\theta_{3}})\,{\dot{\theta}_{3}}+2\,r_{4}\,\cos({\theta_{
465
4}})\,{\dot{\theta}_{4}}+2\,r_{2}\,\cos({\theta_{2}})\,{\dot{\theta}_{
466
2}}+2\,r_{5}\,\cos({\theta_{5}})\,{\dot{\theta}_{5}}+r_{8}\,\cos({
467
\theta_{8}})\,{\dot{\theta}_{8}}\right)^2\right)}{2} \\ &&\quad\mbox{}
468
+ \frac{m_{9}\left(\left(-2\,r_{7}\,\sin({\theta_{7}})\,{\dot{\theta}
469
_{7}}-2\,r_{8}\,\sin({\theta_{8}})\,{\dot{\theta}_{8}}-2\,r_{1}\,\sin(
470
{\theta_{1}})\,{\dot{\theta}_{1}}-2\,r_{6}\,\sin({\theta_{6}})\,{
471
\dot{\theta}_{6}}-2\,r_{5}\,\sin({\theta_{5}})\,{\dot{\theta}_{5}}-2\,
472
r_{3}\,\sin({\theta_{3}})\,{\dot{\theta}_{3}}-2\,r_{2}\,\sin({\theta_{
473
2}})\,{\dot{\theta}_{2}}-2\,r_{4}\,\sin({\theta_{4}})\,{\dot{\theta}_{
474
4}}-r_{9}\,\sin({\theta_{9}})\,{\dot{\theta}_{9}}\right)^2+\left(2\,r
475
_{7}\,\cos({\theta_{7}})\,{\dot{\theta}_{7}}+2\,r_{8}\,\cos({\theta_{8
476
}})\,{\dot{\theta}_{8}}+2\,r_{1}\,\cos({\theta_{1}})\,{\dot{\theta}_{1
477
}}+2\,r_{6}\,\cos({\theta_{6}})\,{\dot{\theta}_{6}}+2\,r_{3}\,\cos({
478
\theta_{3}})\,{\dot{\theta}_{3}}+2\,r_{4}\,\cos({\theta_{4}})\,{
479
\dot{\theta}_{4}}+2\,r_{2}\,\cos({\theta_{2}})\,{\dot{\theta}_{2}}+2\,
480
r_{5}\,\cos({\theta_{5}})\,{\dot{\theta}_{5}}+r_{9}\,\cos({\theta_{9}}
481
)\,{\dot{\theta}_{9}}\right)^2\right)}{2} \\ &&\quad\mbox{} + \frac{m
482
_{6}\left(\left(-2\,r_{1}\,\sin({\theta_{1}})\,{\dot{\theta}_{1}}-2\,r
483
_{5}\,\sin({\theta_{5}})\,{\dot{\theta}_{5}}-2\,r_{3}\,\sin({\theta_{3
484
}})\,{\dot{\theta}_{3}}-2\,r_{2}\,\sin({\theta_{2}})\,{\dot{\theta}_{2
485
}}-2\,r_{4}\,\sin({\theta_{4}})\,{\dot{\theta}_{4}}-r_{6}\,\sin({
486
\theta_{6}})\,{\dot{\theta}_{6}}\right)^2+\left(2\,r_{1}\,\cos({\theta
487
_{1}})\,{\dot{\theta}_{1}}+2\,r_{3}\,\cos({\theta_{3}})\,{\dot{\theta}
488
_{3}}+2\,r_{4}\,\cos({\theta_{4}})\,{\dot{\theta}_{4}}+2\,r_{2}\,\cos(
489
{\theta_{2}})\,{\dot{\theta}_{2}}+2\,r_{5}\,\cos({\theta_{5}})\,{
490
\dot{\theta}_{5}}+r_{6}\,\cos({\theta_{6}})\,{\dot{\theta}_{6}}\right)
491
^2\right)}{2} \end{eqnarray*}
492
$\dot{q}=S(q)\eta$ Kernel of $A(q)'$~:
494
$$ \left( \begin{array}{cccccccccc} -2\,r_{1}\,\sin({\theta_{1}}) & 0
495
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 2\,r_{1}\,\cos({\theta_{1}}) & 0
496
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0
497
& 0 \cr -2\,r_{1}\,\sin({\theta_{1}}) & -2\,r_{2}\,\sin({\theta_{2}})
498
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 2\,r_{1}\,\cos({\theta_{1}}) & 2
499
\,r_{2}\,\cos({\theta_{2}}) & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr 0 & 1
500
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr -2\,r_{1}\,\sin({\theta_{1}}) & -
501
2\,r_{2}\,\sin({\theta_{2}}) & -2\,r_{3}\,\sin({\theta_{3}}) & 0 & 0
502
& 0 & 0 & 0 & 0 & 0 \cr 2\,r_{1}\,\cos({\theta_{1}}) & 2\,r_{2}\,\cos
503
({\theta_{2}}) & 2\,r_{3}\,\cos({\theta_{3}}) & 0 & 0 & 0 & 0 & 0 & 0
504
& 0 \cr 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \cr -2\,r_{1}\,\sin({
505
\theta_{1}}) & -2\,r_{2}\,\sin({\theta_{2}}) & -2\,r_{3}\,\sin({\theta
506
_{3}}) & -2\,r_{4}\,\sin({\theta_{4}}) & 0 & 0 & 0 & 0 & 0 & 0 \cr 2\,
507
r_{1}\,\cos({\theta_{1}}) & 2\,r_{2}\,\cos({\theta_{2}}) & 2\,r_{3}\,
508
\cos({\theta_{3}}) & 2\,r_{4}\,\cos({\theta_{4}}) & 0 & 0 & 0 & 0 & 0
509
& 0 \cr 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \cr -2\,r_{1}\,\sin({
510
\theta_{1}}) & -2\,r_{2}\,\sin({\theta_{2}}) & -2\,r_{3}\,\sin({\theta
511
_{3}}) & -2\,r_{4}\,\sin({\theta_{4}}) & -2\,r_{5}\,\sin({\theta_{5}})
512
& 0 & 0 & 0 & 0 & 0 \cr 2\,r_{1}\,\cos({\theta_{1}}) & 2\,r_{2}\,\cos
513
({\theta_{2}}) & 2\,r_{3}\,\cos({\theta_{3}}) & 2\,r_{4}\,\cos({\theta
514
_{4}}) & 2\,r_{5}\,\cos({\theta_{5}}) & 0 & 0 & 0 & 0 & 0 \cr 0 & 0 &
515
0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \cr -2\,r_{1}\,\sin({\theta_{1}}) & -2\,
516
r_{2}\,\sin({\theta_{2}}) & -2\,r_{3}\,\sin({\theta_{3}}) & -2\,r_{4}
517
\,\sin({\theta_{4}}) & -2\,r_{5}\,\sin({\theta_{5}}) & -2\,r_{6}\,\sin
518
({\theta_{6}}) & 0 & 0 & 0 & 0 \cr 2\,r_{1}\,\cos({\theta_{1}}) & 2\,r
519
_{2}\,\cos({\theta_{2}}) & 2\,r_{3}\,\cos({\theta_{3}}) & 2\,r_{4}\,
520
\cos({\theta_{4}}) & 2\,r_{5}\,\cos({\theta_{5}}) & 2\,r_{6}\,\cos({
521
\theta_{6}}) & 0 & 0 & 0 & 0 \cr 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0
522
\cr -2\,r_{1}\,\sin({\theta_{1}}) & -2\,r_{2}\,\sin({\theta_{2}}) & -
523
2\,r_{3}\,\sin({\theta_{3}}) & -2\,r_{4}\,\sin({\theta_{4}}) & -2\,r_{
524
5}\,\sin({\theta_{5}}) & -2\,r_{6}\,\sin({\theta_{6}}) & -2\,r_{7}\,
525
\sin({\theta_{7}}) & 0 & 0 & 0 \cr 2\,r_{1}\,\cos({\theta_{1}}) & 2\,r
526
_{2}\,\cos({\theta_{2}}) & 2\,r_{3}\,\cos({\theta_{3}}) & 2\,r_{4}\,
527
\cos({\theta_{4}}) & 2\,r_{5}\,\cos({\theta_{5}}) & 2\,r_{6}\,\cos({
528
\theta_{6}}) & 2\,r_{7}\,\cos({\theta_{7}}) & 0 & 0 & 0 \cr 0 & 0 & 0
529
& 0 & 0 & 0 & 1 & 0 & 0 & 0 \cr -2\,r_{1}\,\sin({\theta_{1}}) & -2\,r
530
_{2}\,\sin({\theta_{2}}) & -2\,r_{3}\,\sin({\theta_{3}}) & -2\,r_{4}\,
531
\sin({\theta_{4}}) & -2\,r_{5}\,\sin({\theta_{5}}) & -2\,r_{6}\,\sin({
532
\theta_{6}}) & -2\,r_{7}\,\sin({\theta_{7}}) & -2\,r_{8}\,\sin({\theta
533
_{8}}) & 0 & 0 \cr 2\,r_{1}\,\cos({\theta_{1}}) & 2\,r_{2}\,\cos({
534
\theta_{2}}) & 2\,r_{3}\,\cos({\theta_{3}}) & 2\,r_{4}\,\cos({\theta_{
535
4}}) & 2\,r_{5}\,\cos({\theta_{5}}) & 2\,r_{6}\,\cos({\theta_{6}}) & 2
536
\,r_{7}\,\cos({\theta_{7}}) & 2\,r_{8}\,\cos({\theta_{8}}) & 0 & 0
537
\cr 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \cr -2\,r_{1}\,\sin({\theta
538
_{1}}) & -2\,r_{2}\,\sin({\theta_{2}}) & -2\,r_{3}\,\sin({\theta_{3}})
539
& -2\,r_{4}\,\sin({\theta_{4}}) & -2\,r_{5}\,\sin({\theta_{5}}) & -2
540
\,r_{6}\,\sin({\theta_{6}}) & -2\,r_{7}\,\sin({\theta_{7}}) & -2\,r_{8
541
}\,\sin({\theta_{8}}) & -2\,r_{9}\,\sin({\theta_{9}}) & 0 \cr 2\,r_{1}
542
\,\cos({\theta_{1}}) & 2\,r_{2}\,\cos({\theta_{2}}) & 2\,r_{3}\,\cos({
543
\theta_{3}}) & 2\,r_{4}\,\cos({\theta_{4}}) & 2\,r_{5}\,\cos({\theta_{
544
5}}) & 2\,r_{6}\,\cos({\theta_{6}}) & 2\,r_{7}\,\cos({\theta_{7}}) & 2
545
\,r_{8}\,\cos({\theta_{8}}) & 2\,r_{9}\,\cos({\theta_{9}}) & 0 \cr 0
546
& 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \cr -2\,r_{1}\,\sin({\theta_{1}})
547
& -2\,r_{2}\,\sin({\theta_{2}}) & -2\,r_{3}\,\sin({\theta_{3}}) & -2
548
\,r_{4}\,\sin({\theta_{4}}) & -2\,r_{5}\,\sin({\theta_{5}}) & -2\,r_{6
549
}\,\sin({\theta_{6}}) & -2\,r_{7}\,\sin({\theta_{7}}) & -2\,r_{8}\,
550
\sin({\theta_{8}}) & -2\,r_{9}\,\sin({\theta_{9}}) & -2\,r_{10}\,\sin(
551
{\theta_{10}}) \cr 2\,r_{1}\,\cos({\theta_{1}}) & 2\,r_{2}\,\cos({
552
\theta_{2}}) & 2\,r_{3}\,\cos({\theta_{3}}) & 2\,r_{4}\,\cos({\theta_{
553
4}}) & 2\,r_{5}\,\cos({\theta_{5}}) & 2\,r_{6}\,\cos({\theta_{6}}) & 2
554
\,r_{7}\,\cos({\theta_{7}}) & 2\,r_{8}\,\cos({\theta_{8}}) & 2\,r_{9}
555
\,\cos({\theta_{9}}) & 2\,r_{10}\,\cos({\theta_{10}}) \cr 0 & 0 & 0 &
556
0 & 0 & 0 & 0 & 0 & 0 & 1 \end{array} \right) $$
557
$S(q)^T E$ simplified with $\dot{q}=S(q)\eta $
559
\begin{eqnarray*} && m_{8}\,g\,r_{8}\,\cos({\theta_{8}}) + 4\,{r_{8}}^
560
2\,m_{9}\,{\dot{\eta}_{8}} + 2\,r_{8}\,\cos({\theta_{8}})\,m_{10}\,g
561
+ 2\,r_{8}\,\cos({\theta_{8}})\,m_{9}\,g \\ &&\quad\mbox{} + 4\,r_{8}
562
\,\sin({\theta_{8}})\,m_{10}\,r_{9}\,\cos({\theta_{9}})\,{{\eta_{9}}}^
563
2 + 4\,r_{8}\,\sin({\theta_{8}})\,m_{10}\,r_{9}\,\sin({\theta_{9}})\,{
564
\dot{\eta}_{9}} \\ &&\quad\mbox{} + 4\,r_{8}\,\sin({\theta_{8}})\,m_{
565
10}\,r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{8}\,\sin({
566
\theta_{8}})\,m_{10}\,r_{7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}}
567
\\ &&\quad\mbox{} + 4\,r_{8}\,\sin({\theta_{8}})\,m_{10}\,r_{6}\,\cos
568
({\theta_{6}})\,{{\eta_{6}}}^2 + 4\,r_{8}\,\sin({\theta_{8}})\,m_{10}
569
\,r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} - 4\,r
570
_{8}\,\cos({\theta_{8}})\,m_{10}\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1
571
}}}^2 + 4\,r_{8}\,\cos({\theta_{8}})\,m_{10}\,r_{1}\,\cos({\theta_{1}}
572
)\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} - 4\,r_{8}\,\cos({\theta_{8}})\,
573
m_{10}\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{8}\,\cos({
574
\theta_{8}})\,m_{10}\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}}
575
\\ &&\quad\mbox{} - 4\,r_{8}\,\cos({\theta_{8}})\,m_{10}\,r_{2}\,\sin
576
({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{8}\,\cos({\theta_{8}})\,m_{10}
577
\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} - 4\,r
578
_{8}\,\cos({\theta_{8}})\,m_{10}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4
579
}}}^2 + 4\,r_{8}\,\cos({\theta_{8}})\,m_{10}\,r_{4}\,\cos({\theta_{4}}
580
)\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} - 4\,r_{8}\,\cos({\theta_{8}})\,
581
m_{10}\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{8}\,\cos({
582
\theta_{8}})\,m_{10}\,r_{5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5}}
583
\\ &&\quad\mbox{} - 4\,r_{8}\,\cos({\theta_{8}})\,m_{10}\,r_{9}\,\sin
584
({\theta_{9}})\,{{\eta_{9}}}^2 + 4\,r_{8}\,\cos({\theta_{8}})\,m_{10}
585
\,r_{9}\,\cos({\theta_{9}})\,{\dot{\eta}_{9}} \\ &&\quad\mbox{} - 4\,r
586
_{8}\,\cos({\theta_{8}})\,m_{10}\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7
587
}}}^2 + 4\,r_{8}\,\cos({\theta_{8}})\,m_{9}\,r_{7}\,\cos({\theta_{7}})
588
\,{\dot{\eta}_{7}} \\ &&\quad\mbox{} - 4\,r_{8}\,\cos({\theta_{8}})\,m
589
_{9}\,r_{6}\,\sin({\theta_{6}})\,{{\eta_{6}}}^2 + 4\,r_{8}\,\cos({
590
\theta_{8}})\,m_{9}\,r_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}}
591
\\ &&\quad\mbox{} + 2\,m_{8}\,r_{8}\,\sin({\theta_{8}})\,r_{1}\,\cos(
592
{\theta_{1}})\,{{\eta_{1}}}^2 + 2\,m_{8}\,r_{8}\,\sin({\theta_{8}})\,r
593
_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} + 2\,m_{8
594
}\,r_{8}\,\sin({\theta_{8}})\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^
595
2 + 2\,m_{8}\,r_{8}\,\sin({\theta_{8}})\,r_{4}\,\sin({\theta_{4}})\,{
596
\dot{\eta}_{4}} \\ &&\quad\mbox{} + 2\,m_{8}\,r_{8}\,\sin({\theta_{8}}
597
)\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2 + 2\,m_{8}\,r_{8}\,\sin({
598
\theta_{8}})\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}}
599
\\ &&\quad\mbox{} + 2\,m_{8}\,r_{8}\,\sin({\theta_{8}})\,r_{2}\,\cos(
600
{\theta_{2}})\,{{\eta_{2}}}^2 + 2\,m_{8}\,r_{8}\,\sin({\theta_{8}})\,r
601
_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} - 2\,m_{8
602
}\,r_{8}\,\cos({\theta_{8}})\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^
603
2 + 2\,m_{8}\,r_{8}\,\cos({\theta_{8}})\,r_{5}\,\cos({\theta_{5}})\,{
604
\dot{\eta}_{5}} \\ &&\quad\mbox{} - 2\,m_{8}\,r_{8}\,\cos({\theta_{8}}
605
)\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7}}}^2 + 2\,m_{8}\,r_{8}\,\cos({
606
\theta_{8}})\,r_{7}\,\cos({\theta_{7}})\,{\dot{\eta}_{7}}
607
\\ &&\quad\mbox{} - 2\,m_{8}\,r_{8}\,\cos({\theta_{8}})\,r_{6}\,\sin(
608
{\theta_{6}})\,{{\eta_{6}}}^2 + 2\,m_{8}\,r_{8}\,\cos({\theta_{8}})\,r
609
_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} + 4\,r_{8
610
}\,\sin({\theta_{8}})\,m_{10}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}
611
^2 + 4\,r_{8}\,\sin({\theta_{8}})\,m_{10}\,r_{1}\,\sin({\theta_{1}})\,
612
{\dot{\eta}_{1}} \\ &&\quad\mbox{} + 4\,r_{8}\,\sin({\theta_{8}})\,m_{
613
10}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r_{8}\,\sin({
614
\theta_{8}})\,m_{10}\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}}
615
\\ &&\quad\mbox{} + 4\,r_{8}\,\sin({\theta_{8}})\,m_{10}\,r_{3}\,\cos
616
({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{8}\,\sin({\theta_{8}})\,m_{10}
617
\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,r
618
_{8}\,\sin({\theta_{8}})\,m_{10}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2
619
}}}^2 + 4\,r_{8}\,\sin({\theta_{8}})\,m_{10}\,r_{2}\,\sin({\theta_{2}}
620
)\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} + 4\,r_{8}\,\sin({\theta_{8}})\,
621
m_{10}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{8}\,\sin({
622
\theta_{8}})\,m_{9}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2
623
\\ &&\quad\mbox{} - 4\,r_{8}\,\cos({\theta_{8}})\,m_{10}\,r_{6}\,\sin
624
({\theta_{6}})\,{{\eta_{6}}}^2 + 4\,r_{8}\,\cos({\theta_{8}})\,m_{10}
625
\,r_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} + 4\,r
626
_{8}\,\cos({\theta_{8}})\,m_{10}\,r_{7}\,\cos({\theta_{7}})\,{
627
\dot{\eta}_{7}} + 2\,m_{8}\,r_{8}\,\cos({\theta_{8}})\,r_{2}\,\cos({
628
\theta_{2}})\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} - 2\,m_{8}\,r_{8}\,
629
\cos({\theta_{8}})\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^2 + 2\,m_{
630
8}\,r_{8}\,\cos({\theta_{8}})\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}
631
_{4}} \\ &&\quad\mbox{} + 4\,r_{8}\,\sin({\theta_{8}})\,m_{10}\,r_{5}
632
\,\sin({\theta_{5}})\,{\dot{\eta}_{5}} + 2\,m_{8}\,r_{8}\,\sin({\theta
633
_{8}})\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} +
634
4\,r_{8}\,\sin({\theta_{8}})\,m_{9}\,r_{7}\,\sin({\theta_{7}})\,{
635
\dot{\eta}_{7}} + 4\,r_{8}\,\sin({\theta_{8}})\,m_{9}\,r_{2}\,\cos({
636
\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{8}\,\sin({
637
\theta_{8}})\,m_{9}\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}} + 4\,
638
r_{8}\,\sin({\theta_{8}})\,m_{9}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5
639
}}}^2 \\ &&\quad\mbox{} + 4\,r_{8}\,\sin({\theta_{8}})\,m_{9}\,r_{6}\,
640
\cos({\theta_{6}})\,{{\eta_{6}}}^2 + 4\,r_{8}\,\sin({\theta_{8}})\,m_{
641
9}\,r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} - 4
642
\,r_{8}\,\cos({\theta_{8}})\,m_{9}\,r_{1}\,\sin({\theta_{1}})\,{{\eta
643
_{1}}}^2 + 4\,r_{8}\,\cos({\theta_{8}})\,m_{9}\,r_{1}\,\cos({\theta_{1
644
}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} - 4\,r_{8}\,\cos({\theta_{8}})
645
\,m_{9}\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{8}\,\cos({
646
\theta_{8}})\,m_{9}\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}}
647
\\ &&\quad\mbox{} - 4\,r_{8}\,\cos({\theta_{8}})\,m_{9}\,r_{2}\,\sin(
648
{\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{8}\,\cos({\theta_{8}})\,m_{9}\,r
649
_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} - 4\,r_{8
650
}\,\cos({\theta_{8}})\,m_{9}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^
651
2 + 4\,r_{8}\,\cos({\theta_{8}})\,m_{9}\,r_{4}\,\cos({\theta_{4}})\,{
652
\dot{\eta}_{4}} \\ &&\quad\mbox{} - 4\,r_{8}\,\cos({\theta_{8}})\,m_{9
653
}\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{8}\,\cos({\theta
654
_{8}})\,m_{9}\,r_{5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5}}
655
\\ &&\quad\mbox{} - 4\,r_{8}\,\cos({\theta_{8}})\,m_{9}\,r_{7}\,\sin(
656
{\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{8}\,\sin({\theta_{8}})\,m_{9}\,r
657
_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} + 4\,r_{8
658
}\,\sin({\theta_{8}})\,m_{9}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^
659
2 + 4\,r_{8}\,\sin({\theta_{8}})\,m_{9}\,r_{4}\,\sin({\theta_{4}})\,{
660
\dot{\eta}_{4}} \\ &&\quad\mbox{} + 4\,r_{8}\,\sin({\theta_{8}})\,m_{9
661
}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{8}\,\sin({\theta
662
_{8}})\,m_{9}\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}}
663
\\ &&\quad\mbox{} + 2\,m_{8}\,r_{8}\,\sin({\theta_{8}})\,r_{5}\,\sin(
664
{\theta_{5}})\,{\dot{\eta}_{5}} + 2\,m_{8}\,r_{8}\,\sin({\theta_{8}})
665
\,r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^2 \\ &&\quad\mbox{} + 2\,m_{
666
8}\,r_{8}\,\sin({\theta_{8}})\,r_{7}\,\sin({\theta_{7}})\,{\dot{\eta}
667
_{7}} + 2\,m_{8}\,r_{8}\,\sin({\theta_{8}})\,r_{6}\,\cos({\theta_{6}})
668
\,{{\eta_{6}}}^2 \\ &&\quad\mbox{} + 2\,m_{8}\,r_{8}\,\sin({\theta_{8}
669
})\,r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}_{6}} - 2\,m_{8}\,r_{8}\,
670
\cos({\theta_{8}})\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2
671
\\ &&\quad\mbox{} + 2\,m_{8}\,r_{8}\,\cos({\theta_{8}})\,r_{1}\,\cos(
672
{\theta_{1}})\,{\dot{\eta}_{1}} - 2\,m_{8}\,r_{8}\,\cos({\theta_{8}})
673
\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} + 2\,m_{
674
8}\,r_{8}\,\cos({\theta_{8}})\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}
675
_{3}} - 2\,m_{8}\,r_{8}\,\cos({\theta_{8}})\,r_{2}\,\sin({\theta_{2}})
676
\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{8}\,\sin({\theta_{8}})\,m_{
677
9}\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}} + 4\,r_{8}\,\sin({
678
\theta_{8}})\,m_{9}\,r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^2 + J_{8}
679
\,{\dot{\eta}_{8}} \\ &&\quad\mbox{} + 4\,{r_{8}}^2\,m_{10}\,{
680
\dot{\eta}_{8}} + m_{8}\,{r_{8}}^2\,{\dot{\eta}_{8}} + 2\,r_{8}\,\sin(
681
{\theta_{8}})\,m_{9}\,r_{9}\,\sin({\theta_{9}})\,{\dot{\eta}_{9}}
682
\\ &&\quad\mbox{} + 2\,r_{8}\,\cos({\theta_{8}})\,m_{9}\,r_{9}\,\cos(
683
{\theta_{9}})\,{\dot{\eta}_{9}} + 2\,r_{8}\,\sin({\theta_{8}})\,m_{10}
684
\,r_{10}\,\sin({\theta_{10}})\,{\dot{\eta}_{10}} \\ &&\quad\mbox{} + 2
685
\,r_{8}\,\cos({\theta_{8}})\,m_{10}\,r_{10}\,\cos({\theta_{10}})\,{
686
\dot{\eta}_{10}} + 2\,r_{8}\,\sin({\theta_{8}})\,m_{9}\,r_{9}\,\cos({
687
\theta_{9}})\,{{\eta_{9}}}^2 \\ &&\quad\mbox{} - 2\,r_{8}\,\cos({
688
\theta_{8}})\,m_{9}\,r_{9}\,\sin({\theta_{9}})\,{{\eta_{9}}}^2 + 2\,r
689
_{8}\,\sin({\theta_{8}})\,m_{10}\,r_{10}\,\cos({\theta_{10}})\,{{\eta
690
_{10}}}^2 \\ &&\quad\mbox{} - 2\,r_{8}\,\cos({\theta_{8}})\,m_{10}\,r
691
_{10}\,\sin({\theta_{10}})\,{{\eta_{10}}}^2 \end{eqnarray*}
692
\begin{eqnarray*} && m_{3}\,g\,r_{3}\,\cos({\theta_{3}}) + 2\,r_{3}\,
693
\cos({\theta_{3}})\,m_{5}\,g + 2\,r_{3}\,\cos({\theta_{3}})\,m_{9}\,g
694
+ 2\,r_{3}\,\cos({\theta_{3}})\,m_{4}\,g + 2\,r_{3}\,\cos({\theta_{3}
695
})\,m_{10}\,g \\ &&\quad\mbox{} + 2\,r_{3}\,\cos({\theta_{3}})\,m_{8}
696
\,g + 2\,r_{3}\,\cos({\theta_{3}})\,m_{6}\,g + 2\,r_{3}\,\cos({\theta
697
_{3}})\,m_{7}\,g + 4\,{r_{3}}^2\,m_{8}\,{\dot{\eta}_{3}} + 4\,{r_{3}}^
698
2\,m_{6}\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,{r_{3}}^2\,m_{9}\,{
699
\dot{\eta}_{3}} + 4\,{r_{3}}^2\,m_{5}\,{\dot{\eta}_{3}} + 4\,{r_{3}}^2
700
\,m_{7}\,{\dot{\eta}_{3}} + 4\,{r_{3}}^2\,m_{4}\,{\dot{\eta}_{3}} + J
701
_{3}\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,{r_{3}}^2\,m_{10}\,{
702
\dot{\eta}_{3}} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{6}\,r_{2}\,\sin({
703
\theta_{2}})\,{\dot{\eta}_{2}} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{7}\,
704
r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} + 4\,r_{
705
3}\,\sin({\theta_{3}})\,m_{7}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}
706
^2 + 4\,r_{3}\,\sin({\theta_{3}})\,m_{7}\,r_{5}\,\sin({\theta_{5}})\,{
707
\dot{\eta}_{5}} \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{7
708
}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2 + 4\,r_{3}\,\sin({\theta
709
_{3}})\,m_{7}\,r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}_{6}}
710
\\ &&\quad\mbox{} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{7}\,r_{1}\,\sin(
711
{\theta_{1}})\,{{\eta_{1}}}^2 + 4\,r_{3}\,\cos({\theta_{3}})\,m_{7}\,r
712
_{1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} - 4\,r_{3
713
}\,\cos({\theta_{3}})\,m_{7}\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^
714
2 + 4\,r_{3}\,\cos({\theta_{3}})\,m_{7}\,r_{2}\,\cos({\theta_{2}})\,{
715
\dot{\eta}_{2}} \\ &&\quad\mbox{} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{7
716
}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r_{3}\,\cos({\theta
717
_{3}})\,m_{7}\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}}
718
\\ &&\quad\mbox{} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{7}\,r_{5}\,\sin(
719
{\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{3}\,\cos({\theta_{3}})\,m_{7}\,r
720
_{5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5}} \\ &&\quad\mbox{} - 4\,r_{3
721
}\,\cos({\theta_{3}})\,m_{7}\,r_{6}\,\sin({\theta_{6}})\,{{\eta_{6}}}^
722
2 + 4\,r_{3}\,\cos({\theta_{3}})\,m_{7}\,r_{6}\,\cos({\theta_{6}})\,{
723
\dot{\eta}_{6}} \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{8
724
}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2 + 4\,r_{3}\,\sin({\theta
725
_{3}})\,m_{8}\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}}
726
\\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{8}\,r_{4}\,\cos(
727
{\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r_{3}\,\sin({\theta_{3}})\,m_{8}\,r
728
_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} + 4\,r_{3
729
}\,\sin({\theta_{3}})\,m_{8}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^
730
2 + 4\,r_{3}\,\sin({\theta_{3}})\,m_{8}\,r_{2}\,\sin({\theta_{2}})\,{
731
\dot{\eta}_{2}} \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{8
732
}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{3}\,\sin({\theta
733
_{3}})\,m_{8}\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}}
734
\\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{6}\,r_{5}\,\cos(
735
{\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{3}\,\sin({\theta_{3}})\,m_{6}\,r
736
_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}} \\ &&\quad\mbox{} - 4\,r_{3
737
}\,\cos({\theta_{3}})\,m_{6}\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^
738
2 + 4\,r_{3}\,\cos({\theta_{3}})\,m_{6}\,r_{1}\,\cos({\theta_{1}})\,{
739
\dot{\eta}_{1}} \\ &&\quad\mbox{} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{6
740
}\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{3}\,\cos({\theta
741
_{3}})\,m_{6}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}}
742
\\ &&\quad\mbox{} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{6}\,r_{4}\,\sin(
743
{\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r_{3}\,\cos({\theta_{3}})\,m_{6}\,r
744
_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} - 4\,r_{3
745
}\,\cos({\theta_{3}})\,m_{6}\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^
746
2 + 4\,r_{3}\,\cos({\theta_{3}})\,m_{6}\,r_{5}\,\cos({\theta_{5}})\,{
747
\dot{\eta}_{5}} \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{7
748
}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2 + 4\,r_{3}\,\sin({\theta
749
_{3}})\,m_{7}\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}}
750
\\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{7}\,r_{4}\,\cos(
751
{\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r_{3}\,\sin({\theta_{3}})\,m_{7}\,r
752
_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} + 4\,r_{3
753
}\,\sin({\theta_{3}})\,m_{9}\,r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^
754
2 + 4\,r_{3}\,\sin({\theta_{3}})\,m_{9}\,r_{7}\,\sin({\theta_{7}})\,{
755
\dot{\eta}_{7}} \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{9
756
}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2 + 4\,r_{3}\,\sin({\theta
757
_{3}})\,m_{9}\,r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}_{6}}
758
\\ &&\quad\mbox{} + 2\,r_{3}\,\sin({\theta_{3}})\,m_{8}\,r_{8}\,\sin(
759
{\theta_{8}})\,{\dot{\eta}_{8}} + 2\,r_{3}\,\cos({\theta_{3}})\,m_{8}
760
\,r_{8}\,\cos({\theta_{8}})\,{\dot{\eta}_{8}} \\ &&\quad\mbox{} + 2\,r
761
_{3}\,\cos({\theta_{3}})\,m_{9}\,r_{9}\,\cos({\theta_{9}})\,{
762
\dot{\eta}_{9}} + 2\,r_{3}\,\sin({\theta_{3}})\,m_{9}\,r_{9}\,\sin({
763
\theta_{9}})\,{\dot{\eta}_{9}} \\ &&\quad\mbox{} + 2\,r_{3}\,\sin({
764
\theta_{3}})\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,{\dot{\eta}_{10}}
765
+ 2\,r_{3}\,\cos({\theta_{3}})\,m_{10}\,r_{10}\,\cos({\theta_{10}})\,
766
{\dot{\eta}_{10}} \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m
767
_{4}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{3}\,\sin({
768
\theta_{3}})\,m_{4}\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}}
769
\\ &&\quad\mbox{} + 4\,r_{3}\,\cos({\theta_{3}})\,m_{8}\,r_{1}\,\cos(
770
{\theta_{1}})\,{\dot{\eta}_{1}} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{8}
771
\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{
772
3}\,\cos({\theta_{3}})\,m_{8}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}
773
_{2}} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{8}\,r_{4}\,\sin({\theta_{4}})
774
\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{3}\,\cos({\theta_{3}})\,m_{
775
8}\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}} - 4\,r_{3}\,\cos({
776
\theta_{3}})\,m_{8}\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2
777
\\ &&\quad\mbox{} + 4\,r_{3}\,\cos({\theta_{3}})\,m_{8}\,r_{5}\,\cos(
778
{\theta_{5}})\,{\dot{\eta}_{5}} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{8}
779
\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7}}}^2 \\ &&\quad\mbox{} + 4\,r_{
780
3}\,\cos({\theta_{3}})\,m_{8}\,r_{7}\,\cos({\theta_{7}})\,{\dot{\eta}
781
_{7}} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{8}\,r_{6}\,\sin({\theta_{6}})
782
\,{{\eta_{6}}}^2 \\ &&\quad\mbox{} + 4\,r_{3}\,\cos({\theta_{3}})\,m_{
783
8}\,r_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}} - 4\,r_{3}\,\cos({
784
\theta_{3}})\,m_{9}\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2
785
\\ &&\quad\mbox{} + 4\,r_{3}\,\cos({\theta_{3}})\,m_{9}\,r_{1}\,\cos(
786
{\theta_{1}})\,{\dot{\eta}_{1}} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{9}
787
\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{
788
3}\,\cos({\theta_{3}})\,m_{9}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}
789
_{2}} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{9}\,r_{4}\,\sin({\theta_{4}})
790
\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{3}\,\cos({\theta_{3}})\,m_{
791
9}\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}} + 2\,m_{3}\,r_{3}\,
792
\sin({\theta_{3}})\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2
793
\\ &&\quad\mbox{} + 2\,m_{3}\,r_{3}\,\sin({\theta_{3}})\,r_{1}\,\sin(
794
{\theta_{1}})\,{\dot{\eta}_{1}} + 2\,m_{3}\,r_{3}\,\sin({\theta_{3}})
795
\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 2\,m_{
796
3}\,r_{3}\,\sin({\theta_{3}})\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}
797
_{2}} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{4}\,r_{1}\,\cos({\theta_{1}})
798
\,{{\eta_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{
799
4}\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} + 4\,r_{3}\,\cos({
800
\theta_{3}})\,m_{10}\,r_{1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1}}
801
\\ &&\quad\mbox{} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{10}\,r_{2}\,\sin
802
({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{3}\,\cos({\theta_{3}})\,m_{10}
803
\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} - 4\,r
804
_{3}\,\cos({\theta_{3}})\,m_{10}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4
805
}}}^2 + 4\,r_{3}\,\cos({\theta_{3}})\,m_{10}\,r_{4}\,\cos({\theta_{4}}
806
)\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} - 4\,r_{3}\,\cos({\theta_{3}})\,
807
m_{10}\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{3}\,\cos({
808
\theta_{3}})\,m_{10}\,r_{5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5}}
809
\\ &&\quad\mbox{} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{10}\,r_{8}\,\sin
810
({\theta_{8}})\,{{\eta_{8}}}^2 + 4\,r_{3}\,\cos({\theta_{3}})\,m_{10}
811
\,r_{8}\,\cos({\theta_{8}})\,{\dot{\eta}_{8}} \\ &&\quad\mbox{} - 4\,r
812
_{3}\,\cos({\theta_{3}})\,m_{10}\,r_{9}\,\sin({\theta_{9}})\,{{\eta_{9
813
}}}^2 + 4\,r_{3}\,\cos({\theta_{3}})\,m_{10}\,r_{9}\,\cos({\theta_{9}}
814
)\,{\dot{\eta}_{9}} \\ &&\quad\mbox{} - 4\,r_{3}\,\cos({\theta_{3}})\,
815
m_{10}\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{3}\,\cos({
816
\theta_{3}})\,m_{10}\,r_{7}\,\cos({\theta_{7}})\,{\dot{\eta}_{7}}
817
\\ &&\quad\mbox{} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{10}\,r_{6}\,\sin
818
({\theta_{6}})\,{{\eta_{6}}}^2 + 4\,r_{3}\,\cos({\theta_{3}})\,m_{10}
819
\,r_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} + 4\,r
820
_{3}\,\sin({\theta_{3}})\,m_{6}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}
821
}}^2 + 4\,r_{3}\,\sin({\theta_{3}})\,m_{6}\,r_{1}\,\sin({\theta_{1}})
822
\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m
823
_{6}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r_{3}\,\sin({
824
\theta_{3}})\,m_{6}\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}}
825
\\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{6}\,r_{2}\,\cos(
826
{\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{3}\,\cos({\theta_{3}})\,m_{9}\,r
827
_{5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5}} \\ &&\quad\mbox{} - 4\,r_{3
828
}\,\cos({\theta_{3}})\,m_{9}\,r_{8}\,\sin({\theta_{8}})\,{{\eta_{8}}}^
829
2 + 4\,r_{3}\,\cos({\theta_{3}})\,m_{9}\,r_{8}\,\cos({\theta_{8}})\,{
830
\dot{\eta}_{8}} \\ &&\quad\mbox{} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{9
831
}\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{3}\,\cos({\theta
832
_{3}})\,m_{9}\,r_{7}\,\cos({\theta_{7}})\,{\dot{\eta}_{7}}
833
\\ &&\quad\mbox{} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{9}\,r_{6}\,\sin(
834
{\theta_{6}})\,{{\eta_{6}}}^2 + 4\,r_{3}\,\cos({\theta_{3}})\,m_{9}\,r
835
_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} + 4\,r_{3
836
}\,\sin({\theta_{3}})\,m_{9}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^
837
2 + 4\,r_{3}\,\sin({\theta_{3}})\,m_{9}\,r_{1}\,\sin({\theta_{1}})\,{
838
\dot{\eta}_{1}} \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{9
839
}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r_{3}\,\sin({\theta
840
_{3}})\,m_{9}\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}}
841
\\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{9}\,r_{2}\,\cos(
842
{\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{3}\,\sin({\theta_{3}})\,m_{9}\,r
843
_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} + 4\,r_{3
844
}\,\sin({\theta_{3}})\,m_{9}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^
845
2 + 4\,r_{3}\,\sin({\theta_{3}})\,m_{9}\,r_{5}\,\sin({\theta_{5}})\,{
846
\dot{\eta}_{5}} \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{9
847
}\,r_{8}\,\cos({\theta_{8}})\,{{\eta_{8}}}^2 - 4\,r_{3}\,\cos({\theta
848
_{3}})\,m_{4}\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2
849
\\ &&\quad\mbox{} + 4\,r_{3}\,\cos({\theta_{3}})\,m_{4}\,r_{1}\,\cos(
850
{\theta_{1}})\,{\dot{\eta}_{1}} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{4}
851
\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{
852
3}\,\cos({\theta_{3}})\,m_{4}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}
853
_{2}} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{5}\,r_{1}\,\cos({\theta_{1}})
854
\,{{\eta_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{
855
5}\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} + 4\,r_{3}\,\sin({
856
\theta_{3}})\,m_{5}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^2
857
\\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{5}\,r_{4}\,\sin(
858
{\theta_{4}})\,{\dot{\eta}_{4}} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{5}
859
\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{
860
3}\,\sin({\theta_{3}})\,m_{5}\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}
861
_{2}} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{5}\,r_{1}\,\sin({\theta_{1}})
862
\,{{\eta_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{3}\,\cos({\theta_{3}})\,m_{
863
5}\,r_{1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1}} - 4\,r_{3}\,\cos({
864
\theta_{3}})\,m_{5}\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2
865
\\ &&\quad\mbox{} + 4\,r_{3}\,\cos({\theta_{3}})\,m_{5}\,r_{2}\,\cos(
866
{\theta_{2}})\,{\dot{\eta}_{2}} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{5}
867
\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{
868
3}\,\cos({\theta_{3}})\,m_{5}\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}
869
_{4}} - 2\,m_{3}\,r_{3}\,\cos({\theta_{3}})\,r_{1}\,\sin({\theta_{1}})
870
\,{{\eta_{1}}}^2 \\ &&\quad\mbox{} + 2\,m_{3}\,r_{3}\,\cos({\theta_{3}
871
})\,r_{1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1}} - 2\,m_{3}\,r_{3}\,
872
\cos({\theta_{3}})\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2
873
\\ &&\quad\mbox{} + 2\,m_{3}\,r_{3}\,\cos({\theta_{3}})\,r_{2}\,\cos(
874
{\theta_{2}})\,{\dot{\eta}_{2}} - 4\,r_{3}\,\cos({\theta_{3}})\,m_{10}
875
\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2 \\ &&\quad\mbox{} - 4\,r_{
876
3}\,\cos({\theta_{3}})\,m_{8}\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}
877
^2 + 4\,r_{3}\,\sin({\theta_{3}})\,m_{8}\,r_{7}\,\cos({\theta_{7}})\,{
878
{\eta_{7}}}^2 \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{10}
879
\,r_{7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}} + 4\,r_{3}\,\sin({\theta
880
_{3}})\,m_{10}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2
881
\\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{10}\,r_{6}\,\sin
882
({\theta_{6}})\,{\dot{\eta}_{6}} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{8}
883
\,r_{7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}} \\ &&\quad\mbox{} + 4\,r
884
_{3}\,\sin({\theta_{3}})\,m_{8}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}
885
}}^2 + 4\,r_{3}\,\sin({\theta_{3}})\,m_{8}\,r_{6}\,\sin({\theta_{6}})
886
\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m
887
_{10}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2 + 4\,r_{3}\,\sin({
888
\theta_{3}})\,m_{10}\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}}
889
\\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{10}\,r_{4}\,\cos
890
({\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r_{3}\,\sin({\theta_{3}})\,m_{10}
891
\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} + 4\,r
892
_{3}\,\sin({\theta_{3}})\,m_{10}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2
893
}}}^2 + 4\,r_{3}\,\sin({\theta_{3}})\,m_{10}\,r_{2}\,\sin({\theta_{2}}
894
)\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,
895
m_{10}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{3}\,\sin({
896
\theta_{3}})\,m_{10}\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}}
897
\\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,m_{10}\,r_{9}\,\cos
898
({\theta_{9}})\,{{\eta_{9}}}^2 + 4\,r_{3}\,\sin({\theta_{3}})\,m_{10}
899
\,r_{9}\,\sin({\theta_{9}})\,{\dot{\eta}_{9}} \\ &&\quad\mbox{} + 4\,r
900
_{3}\,\sin({\theta_{3}})\,m_{10}\,r_{8}\,\cos({\theta_{8}})\,{{\eta_{8
901
}}}^2 + 4\,r_{3}\,\sin({\theta_{3}})\,m_{10}\,r_{8}\,\sin({\theta_{8}}
902
)\,{\dot{\eta}_{8}} \\ &&\quad\mbox{} + 4\,r_{3}\,\sin({\theta_{3}})\,
903
m_{10}\,r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{3}\,\sin({
904
\theta_{3}})\,m_{7}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 + m_{3}
905
\,{r_{3}}^2\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} - 4\,r_{3}\,\cos({
906
\theta_{3}})\,m_{9}\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r
907
_{3}\,\sin({\theta_{3}})\,m_{9}\,r_{8}\,\sin({\theta_{8}})\,{
908
\dot{\eta}_{8}} \\ &&\quad\mbox{} + 2\,r_{3}\,\sin({\theta_{3}})\,m_{4
909
}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^2 - 2\,r_{3}\,\cos({\theta
910
_{3}})\,m_{4}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^2
911
\\ &&\quad\mbox{} - 2\,r_{3}\,\cos({\theta_{3}})\,m_{5}\,r_{5}\,\sin(
912
{\theta_{5}})\,{{\eta_{5}}}^2 + 2\,r_{3}\,\sin({\theta_{3}})\,m_{5}\,r
913
_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 2\,r_{3}
914
\,\sin({\theta_{3}})\,m_{6}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2
915
- 2\,r_{3}\,\cos({\theta_{3}})\,m_{6}\,r_{6}\,\sin({\theta_{6}})\,{{
916
\eta_{6}}}^2 \\ &&\quad\mbox{} + 2\,r_{3}\,\sin({\theta_{3}})\,m_{7}\,
917
r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^2 - 2\,r_{3}\,\cos({\theta_{3}
918
})\,m_{7}\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7}}}^2 \\ &&\quad\mbox{}
919
- 2\,r_{3}\,\cos({\theta_{3}})\,m_{8}\,r_{8}\,\sin({\theta_{8}})\,{{
920
\eta_{8}}}^2 + 2\,r_{3}\,\sin({\theta_{3}})\,m_{8}\,r_{8}\,\cos({
921
\theta_{8}})\,{{\eta_{8}}}^2 \\ &&\quad\mbox{} - 2\,r_{3}\,\cos({
922
\theta_{3}})\,m_{9}\,r_{9}\,\sin({\theta_{9}})\,{{\eta_{9}}}^2 + 2\,r
923
_{3}\,\sin({\theta_{3}})\,m_{9}\,r_{9}\,\cos({\theta_{9}})\,{{\eta_{9}
924
}}^2 \\ &&\quad\mbox{} + 2\,r_{3}\,\sin({\theta_{3}})\,m_{10}\,r_{10}
925
\,\cos({\theta_{10}})\,{{\eta_{10}}}^2 - 2\,r_{3}\,\cos({\theta_{3}})
926
\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,{{\eta_{10}}}^2
927
\\ &&\quad\mbox{} + 2\,r_{3}\,\sin({\theta_{3}})\,m_{4}\,r_{4}\,\sin(
928
{\theta_{4}})\,{\dot{\eta}_{4}} + 2\,r_{3}\,\cos({\theta_{3}})\,m_{4}
929
\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} + 2\,r
930
_{3}\,\cos({\theta_{3}})\,m_{5}\,r_{5}\,\cos({\theta_{5}})\,{
931
\dot{\eta}_{5}} + 2\,r_{3}\,\sin({\theta_{3}})\,m_{5}\,r_{5}\,\sin({
932
\theta_{5}})\,{\dot{\eta}_{5}} \\ &&\quad\mbox{} + 2\,r_{3}\,\sin({
933
\theta_{3}})\,m_{6}\,r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}_{6}} + 2\,
934
r_{3}\,\cos({\theta_{3}})\,m_{6}\,r_{6}\,\cos({\theta_{6}})\,{
935
\dot{\eta}_{6}} \\ &&\quad\mbox{} + 2\,r_{3}\,\sin({\theta_{3}})\,m_{7
936
}\,r_{7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}} + 2\,r_{3}\,\cos({
937
\theta_{3}})\,m_{7}\,r_{7}\,\cos({\theta_{7}})\,{\dot{\eta}_{7}}
939
\begin{eqnarray*} && 4\,{r_{6}}^2\,m_{7}\,{\dot{\eta}_{6}} + 4\,{r_{6}
940
}^2\,m_{10}\,{\dot{\eta}_{6}} + m_{6}\,g\,r_{6}\,\cos({\theta_{6}}) +
941
4\,{r_{6}}^2\,m_{8}\,{\dot{\eta}_{6}} + 4\,{r_{6}}^2\,m_{9}\,{
942
\dot{\eta}_{6}} \\ &&\quad\mbox{} + 2\,r_{6}\,\cos({\theta_{6}})\,m_{9
943
}\,g + 2\,r_{6}\,\cos({\theta_{6}})\,m_{10}\,g + 2\,r_{6}\,\cos({
944
\theta_{6}})\,m_{7}\,g + 2\,r_{6}\,\cos({\theta_{6}})\,m_{8}\,g
945
\\ &&\quad\mbox{} + 4\,r_{6}\,\sin({\theta_{6}})\,m_{10}\,r_{1}\,\sin
946
({\theta_{1}})\,{\dot{\eta}_{1}} + 4\,r_{6}\,\sin({\theta_{6}})\,m_{10
947
}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r
948
_{6}\,\sin({\theta_{6}})\,m_{10}\,r_{4}\,\sin({\theta_{4}})\,{
949
\dot{\eta}_{4}} + 4\,r_{6}\,\sin({\theta_{6}})\,m_{7}\,r_{3}\,\cos({
950
\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} + 4\,r_{6}\,\sin({
951
\theta_{6}})\,m_{9}\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} + 4\,
952
r_{6}\,\sin({\theta_{6}})\,m_{10}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{
953
1}}}^2 + J_{6}\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} + 2\,r_{6}\,\sin({
954
\theta_{6}})\,m_{8}\,r_{8}\,\sin({\theta_{8}})\,{\dot{\eta}_{8}} + 2\,
955
r_{6}\,\cos({\theta_{6}})\,m_{8}\,r_{8}\,\cos({\theta_{8}})\,{
956
\dot{\eta}_{8}} \\ &&\quad\mbox{} + 2\,r_{6}\,\sin({\theta_{6}})\,m_{9
957
}\,r_{9}\,\sin({\theta_{9}})\,{\dot{\eta}_{9}} + 2\,r_{6}\,\cos({
958
\theta_{6}})\,m_{9}\,r_{9}\,\cos({\theta_{9}})\,{\dot{\eta}_{9}}
959
\\ &&\quad\mbox{} + 2\,r_{6}\,\sin({\theta_{6}})\,m_{10}\,r_{10}\,
960
\sin({\theta_{10}})\,{\dot{\eta}_{10}} + 2\,r_{6}\,\cos({\theta_{6}})
961
\,m_{10}\,r_{10}\,\cos({\theta_{10}})\,{\dot{\eta}_{10}}
962
\\ &&\quad\mbox{} - 2\,r_{6}\,\cos({\theta_{6}})\,m_{7}\,r_{7}\,\sin(
963
{\theta_{7}})\,{{\eta_{7}}}^2 + 2\,r_{6}\,\sin({\theta_{6}})\,m_{7}\,r
964
_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^2 \\ &&\quad\mbox{} + 2\,r_{6}
965
\,\sin({\theta_{6}})\,m_{8}\,r_{8}\,\cos({\theta_{8}})\,{{\eta_{8}}}^2
966
- 2\,r_{6}\,\cos({\theta_{6}})\,m_{8}\,r_{8}\,\sin({\theta_{8}})\,{{
967
\eta_{8}}}^2 \\ &&\quad\mbox{} - 2\,r_{6}\,\cos({\theta_{6}})\,m_{9}\,
968
r_{9}\,\sin({\theta_{9}})\,{{\eta_{9}}}^2 + 2\,r_{6}\,\sin({\theta_{6}
969
})\,m_{9}\,r_{9}\,\cos({\theta_{9}})\,{{\eta_{9}}}^2 \\ &&\quad\mbox{}
970
+ 2\,r_{6}\,\sin({\theta_{6}})\,m_{10}\,r_{10}\,\cos({\theta_{10}})\,
971
{{\eta_{10}}}^2 - 2\,r_{6}\,\cos({\theta_{6}})\,m_{10}\,r_{10}\,\sin({
972
\theta_{10}})\,{{\eta_{10}}}^2 + m_{6}\,{r_{6}}^2\,{\dot{\eta}_{6}}
973
\\ &&\quad\mbox{} + 2\,r_{6}\,\cos({\theta_{6}})\,m_{7}\,r_{7}\,\cos(
974
{\theta_{7}})\,{\dot{\eta}_{7}} + 2\,r_{6}\,\sin({\theta_{6}})\,m_{7}
975
\,r_{7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}} \\ &&\quad\mbox{} + 4\,r
976
_{6}\,\sin({\theta_{6}})\,m_{9}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}
977
}}^2 + 4\,r_{6}\,\sin({\theta_{6}})\,m_{7}\,r_{3}\,\sin({\theta_{3}})
978
\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,r_{6}\,\sin({\theta_{6}})\,m
979
_{7}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{6}\,\sin({
980
\theta_{6}})\,m_{7}\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}}
981
\\ &&\quad\mbox{} + 2\,m_{6}\,r_{6}\,\sin({\theta_{6}})\,r_{1}\,\cos(
982
{\theta_{1}})\,{{\eta_{1}}}^2 + 2\,m_{6}\,r_{6}\,\sin({\theta_{6}})\,r
983
_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} + 4\,r_{6
984
}\,\sin({\theta_{6}})\,m_{7}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^
985
2 + 4\,r_{6}\,\sin({\theta_{6}})\,m_{7}\,r_{1}\,\sin({\theta_{1}})\,{
986
\dot{\eta}_{1}} \\ &&\quad\mbox{} + 4\,r_{6}\,\sin({\theta_{6}})\,m_{7
987
}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r_{6}\,\sin({\theta
988
_{6}})\,m_{7}\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}}
989
\\ &&\quad\mbox{} + 4\,r_{6}\,\sin({\theta_{6}})\,m_{8}\,r_{1}\,\cos(
990
{\theta_{1}})\,{{\eta_{1}}}^2 + 4\,r_{6}\,\sin({\theta_{6}})\,m_{8}\,r
991
_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} + 4\,r_{6
992
}\,\sin({\theta_{6}})\,m_{8}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^
993
2 - 4\,r_{6}\,\cos({\theta_{6}})\,m_{10}\,r_{1}\,\sin({\theta_{1}})\,{
994
{\eta_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{6}\,\cos({\theta_{6}})\,m_{10}
995
\,r_{1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1}} - 4\,r_{6}\,\cos({\theta
996
_{6}})\,m_{10}\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2
997
\\ &&\quad\mbox{} + 4\,r_{6}\,\cos({\theta_{6}})\,m_{10}\,r_{3}\,\cos
998
({\theta_{3}})\,{\dot{\eta}_{3}} - 4\,r_{6}\,\cos({\theta_{6}})\,m_{10
999
}\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r
1000
_{6}\,\cos({\theta_{6}})\,m_{10}\,r_{2}\,\cos({\theta_{2}})\,{
1001
\dot{\eta}_{2}} - 4\,r_{6}\,\cos({\theta_{6}})\,m_{10}\,r_{4}\,\sin({
1002
\theta_{4}})\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{6}\,\cos({
1003
\theta_{6}})\,m_{10}\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}} - 4
1004
\,r_{6}\,\cos({\theta_{6}})\,m_{10}\,r_{5}\,\sin({\theta_{5}})\,{{\eta
1005
_{5}}}^2 \\ &&\quad\mbox{} + 4\,r_{6}\,\cos({\theta_{6}})\,m_{10}\,r_{
1006
5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5}} - 4\,r_{6}\,\cos({\theta_{6}}
1007
)\,m_{10}\,r_{8}\,\sin({\theta_{8}})\,{{\eta_{8}}}^2 \\ &&\quad\mbox{}
1008
+ 4\,r_{6}\,\cos({\theta_{6}})\,m_{10}\,r_{8}\,\cos({\theta_{8}})\,{
1009
\dot{\eta}_{8}} - 4\,r_{6}\,\cos({\theta_{6}})\,m_{10}\,r_{9}\,\sin({
1010
\theta_{9}})\,{{\eta_{9}}}^2 \\ &&\quad\mbox{} + 4\,r_{6}\,\cos({
1011
\theta_{6}})\,m_{10}\,r_{9}\,\cos({\theta_{9}})\,{\dot{\eta}_{9}} - 4
1012
\,r_{6}\,\cos({\theta_{6}})\,m_{10}\,r_{7}\,\sin({\theta_{7}})\,{{\eta
1013
_{7}}}^2 \\ &&\quad\mbox{} + 4\,r_{6}\,\cos({\theta_{6}})\,m_{10}\,r_{
1014
7}\,\cos({\theta_{7}})\,{\dot{\eta}_{7}} - 4\,r_{6}\,\cos({\theta_{6}}
1015
)\,m_{8}\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2 \\ &&\quad\mbox{}
1016
+ 4\,r_{6}\,\cos({\theta_{6}})\,m_{8}\,r_{1}\,\cos({\theta_{1}})\,{
1017
\dot{\eta}_{1}} - 4\,r_{6}\,\cos({\theta_{6}})\,m_{8}\,r_{3}\,\sin({
1018
\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} + 4\,r_{6}\,\cos({
1019
\theta_{6}})\,m_{8}\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}} - 4\,
1020
r_{6}\,\cos({\theta_{6}})\,m_{8}\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2
1021
}}}^2 \\ &&\quad\mbox{} + 4\,r_{6}\,\cos({\theta_{6}})\,m_{8}\,r_{2}\,
1022
\cos({\theta_{2}})\,{\dot{\eta}_{2}} - 4\,r_{6}\,\cos({\theta_{6}})\,m
1023
_{8}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4
1024
\,r_{6}\,\cos({\theta_{6}})\,m_{8}\,r_{4}\,\cos({\theta_{4}})\,{
1025
\dot{\eta}_{4}} - 4\,r_{6}\,\cos({\theta_{6}})\,m_{8}\,r_{5}\,\sin({
1026
\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 4\,r_{6}\,\cos({
1027
\theta_{6}})\,m_{8}\,r_{5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5}} - 4\,
1028
r_{6}\,\cos({\theta_{6}})\,m_{8}\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7
1029
}}}^2 \\ &&\quad\mbox{} + 4\,r_{6}\,\cos({\theta_{6}})\,m_{8}\,r_{7}\,
1030
\cos({\theta_{7}})\,{\dot{\eta}_{7}} + 4\,r_{6}\,\sin({\theta_{6}})\,m
1031
_{7}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 4
1032
\,r_{6}\,\sin({\theta_{6}})\,m_{7}\,r_{5}\,\sin({\theta_{5}})\,{
1033
\dot{\eta}_{5}} + 2\,m_{6}\,r_{6}\,\sin({\theta_{6}})\,r_{4}\,\cos({
1034
\theta_{4}})\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 2\,m_{6}\,r_{6}\,\sin
1035
({\theta_{6}})\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}} + 2\,m_{6}
1036
\,r_{6}\,\sin({\theta_{6}})\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2
1037
\\ &&\quad\mbox{} + 2\,m_{6}\,r_{6}\,\sin({\theta_{6}})\,r_{3}\,\sin(
1038
{\theta_{3}})\,{\dot{\eta}_{3}} + 2\,m_{6}\,r_{6}\,\sin({\theta_{6}})
1039
\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 2\,m_{
1040
6}\,r_{6}\,\sin({\theta_{6}})\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}
1041
_{2}} + 2\,m_{6}\,r_{6}\,\sin({\theta_{6}})\,r_{5}\,\cos({\theta_{5}})
1042
\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 2\,m_{6}\,r_{6}\,\sin({\theta_{6}
1043
})\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}} - 4\,r_{6}\,\cos({
1044
\theta_{6}})\,m_{7}\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2
1045
\\ &&\quad\mbox{} + 4\,r_{6}\,\cos({\theta_{6}})\,m_{7}\,r_{1}\,\cos(
1046
{\theta_{1}})\,{\dot{\eta}_{1}} - 4\,r_{6}\,\cos({\theta_{6}})\,m_{7}
1047
\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} + 4\,r_{
1048
6}\,\cos({\theta_{6}})\,m_{7}\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}
1049
_{3}} - 4\,r_{6}\,\cos({\theta_{6}})\,m_{7}\,r_{2}\,\sin({\theta_{2}})
1050
\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{6}\,\cos({\theta_{6}})\,m_{
1051
7}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}} - 4\,r_{6}\,\cos({
1052
\theta_{6}})\,m_{7}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^2
1053
\\ &&\quad\mbox{} + 4\,r_{6}\,\cos({\theta_{6}})\,m_{7}\,r_{4}\,\cos(
1054
{\theta_{4}})\,{\dot{\eta}_{4}} - 4\,r_{6}\,\cos({\theta_{6}})\,m_{7}
1055
\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 4\,r_{
1056
6}\,\cos({\theta_{6}})\,m_{7}\,r_{5}\,\cos({\theta_{5}})\,{\dot{\eta}
1057
_{5}} + 4\,r_{6}\,\sin({\theta_{6}})\,m_{8}\,r_{4}\,\sin({\theta_{4}})
1058
\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} + 4\,r_{6}\,\sin({\theta_{6}})\,m
1059
_{8}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{6}\,\sin({
1060
\theta_{6}})\,m_{8}\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}}
1061
\\ &&\quad\mbox{} + 4\,r_{6}\,\sin({\theta_{6}})\,m_{8}\,r_{2}\,\cos(
1062
{\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{6}\,\sin({\theta_{6}})\,m_{8}\,r
1063
_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} + 4\,r_{6
1064
}\,\sin({\theta_{6}})\,m_{8}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^
1065
2 + 4\,r_{6}\,\sin({\theta_{6}})\,m_{8}\,r_{5}\,\sin({\theta_{5}})\,{
1066
\dot{\eta}_{5}} \\ &&\quad\mbox{} + 4\,r_{6}\,\sin({\theta_{6}})\,m_{8
1067
}\,r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{6}\,\sin({\theta
1068
_{6}})\,m_{8}\,r_{7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}}
1069
\\ &&\quad\mbox{} - 2\,m_{6}\,r_{6}\,\cos({\theta_{6}})\,r_{1}\,\sin(
1070
{\theta_{1}})\,{{\eta_{1}}}^2 + 2\,m_{6}\,r_{6}\,\cos({\theta_{6}})\,r
1071
_{1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} - 2\,m_{6
1072
}\,r_{6}\,\cos({\theta_{6}})\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^
1073
2 + 2\,m_{6}\,r_{6}\,\cos({\theta_{6}})\,r_{3}\,\cos({\theta_{3}})\,{
1074
\dot{\eta}_{3}} \\ &&\quad\mbox{} - 2\,m_{6}\,r_{6}\,\cos({\theta_{6}}
1075
)\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2 + 2\,m_{6}\,r_{6}\,\cos({
1076
\theta_{6}})\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}}
1077
\\ &&\quad\mbox{} - 2\,m_{6}\,r_{6}\,\cos({\theta_{6}})\,r_{4}\,\sin(
1078
{\theta_{4}})\,{{\eta_{4}}}^2 + 2\,m_{6}\,r_{6}\,\cos({\theta_{6}})\,r
1079
_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} - 2\,m_{6
1080
}\,r_{6}\,\cos({\theta_{6}})\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^
1081
2 + 2\,m_{6}\,r_{6}\,\cos({\theta_{6}})\,r_{5}\,\cos({\theta_{5}})\,{
1082
\dot{\eta}_{5}} \\ &&\quad\mbox{} - 4\,r_{6}\,\cos({\theta_{6}})\,m_{9
1083
}\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2 + 4\,r_{6}\,\cos({\theta
1084
_{6}})\,m_{9}\,r_{1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1}}
1085
\\ &&\quad\mbox{} - 4\,r_{6}\,\cos({\theta_{6}})\,m_{9}\,r_{3}\,\sin(
1086
{\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{6}\,\cos({\theta_{6}})\,m_{9}\,r
1087
_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} - 4\,r_{6
1088
}\,\cos({\theta_{6}})\,m_{9}\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^
1089
2 + 4\,r_{6}\,\cos({\theta_{6}})\,m_{9}\,r_{2}\,\cos({\theta_{2}})\,{
1090
\dot{\eta}_{2}} \\ &&\quad\mbox{} - 4\,r_{6}\,\cos({\theta_{6}})\,m_{9
1091
}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r_{6}\,\cos({\theta
1092
_{6}})\,m_{9}\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}}
1093
\\ &&\quad\mbox{} - 4\,r_{6}\,\cos({\theta_{6}})\,m_{9}\,r_{5}\,\sin(
1094
{\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{6}\,\cos({\theta_{6}})\,m_{9}\,r
1095
_{5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5}} \\ &&\quad\mbox{} - 4\,r_{6
1096
}\,\cos({\theta_{6}})\,m_{9}\,r_{8}\,\sin({\theta_{8}})\,{{\eta_{8}}}^
1097
2 + 4\,r_{6}\,\cos({\theta_{6}})\,m_{9}\,r_{8}\,\cos({\theta_{8}})\,{
1098
\dot{\eta}_{8}} \\ &&\quad\mbox{} - 4\,r_{6}\,\cos({\theta_{6}})\,m_{9
1099
}\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{6}\,\cos({\theta
1100
_{6}})\,m_{9}\,r_{7}\,\cos({\theta_{7}})\,{\dot{\eta}_{7}}
1101
\\ &&\quad\mbox{} + 4\,r_{6}\,\sin({\theta_{6}})\,m_{9}\,r_{4}\,\cos(
1102
{\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r_{6}\,\sin({\theta_{6}})\,m_{9}\,r
1103
_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} + 4\,r_{6
1104
}\,\sin({\theta_{6}})\,m_{9}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^
1105
2 + 4\,r_{6}\,\sin({\theta_{6}})\,m_{9}\,r_{3}\,\sin({\theta_{3}})\,{
1106
\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,r_{6}\,\sin({\theta_{6}})\,m_{9
1107
}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{6}\,\sin({\theta
1108
_{6}})\,m_{9}\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}}
1109
\\ &&\quad\mbox{} + 4\,r_{6}\,\sin({\theta_{6}})\,m_{9}\,r_{5}\,\cos(
1110
{\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{6}\,\sin({\theta_{6}})\,m_{9}\,r
1111
_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}} \\ &&\quad\mbox{} + 4\,r_{6
1112
}\,\sin({\theta_{6}})\,m_{9}\,r_{8}\,\cos({\theta_{8}})\,{{\eta_{8}}}^
1113
2 + 4\,r_{6}\,\sin({\theta_{6}})\,m_{9}\,r_{8}\,\sin({\theta_{8}})\,{
1114
\dot{\eta}_{8}} \\ &&\quad\mbox{} + 4\,r_{6}\,\sin({\theta_{6}})\,m_{9
1115
}\,r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{6}\,\sin({\theta
1116
_{6}})\,m_{9}\,r_{7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}}
1117
\\ &&\quad\mbox{} + 4\,r_{6}\,\sin({\theta_{6}})\,m_{10}\,r_{3}\,\cos
1118
({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{6}\,\sin({\theta_{6}})\,m_{10}
1119
\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,r
1120
_{6}\,\sin({\theta_{6}})\,m_{10}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2
1121
}}}^2 + 4\,r_{6}\,\sin({\theta_{6}})\,m_{10}\,r_{2}\,\sin({\theta_{2}}
1122
)\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} + 4\,r_{6}\,\sin({\theta_{6}})\,
1123
m_{10}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{6}\,\sin({
1124
\theta_{6}})\,m_{10}\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}}
1125
\\ &&\quad\mbox{} + 4\,r_{6}\,\sin({\theta_{6}})\,m_{10}\,r_{9}\,\cos
1126
({\theta_{9}})\,{{\eta_{9}}}^2 + 4\,r_{6}\,\sin({\theta_{6}})\,m_{10}
1127
\,r_{9}\,\sin({\theta_{9}})\,{\dot{\eta}_{9}} \\ &&\quad\mbox{} + 4\,r
1128
_{6}\,\sin({\theta_{6}})\,m_{10}\,r_{8}\,\cos({\theta_{8}})\,{{\eta_{8
1129
}}}^2 + 4\,r_{6}\,\sin({\theta_{6}})\,m_{10}\,r_{8}\,\sin({\theta_{8}}
1130
)\,{\dot{\eta}_{8}} \\ &&\quad\mbox{} + 4\,r_{6}\,\sin({\theta_{6}})\,
1131
m_{10}\,r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{6}\,\sin({
1132
\theta_{6}})\,m_{10}\,r_{7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}}
1134
\begin{eqnarray*} && m_{9}\,g\,r_{9}\,\cos({\theta_{9}}) + 2\,r_{9}\,
1135
\cos({\theta_{9}})\,m_{10}\,g + J_{9}\,{\dot{\eta}_{9}} + m_{9}\,{r_{9
1136
}}^2\,{\dot{\eta}_{9}} \\ &&\quad\mbox{} + 2\,r_{9}\,\sin({\theta_{9}}
1137
)\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,{\dot{\eta}_{10}} + 2\,r_{9}\,
1138
\cos({\theta_{9}})\,m_{10}\,r_{10}\,\cos({\theta_{10}})\,{\dot{\eta}_{
1139
10}} \\ &&\quad\mbox{} + 2\,r_{9}\,\sin({\theta_{9}})\,m_{10}\,r_{10}
1140
\,\cos({\theta_{10}})\,{{\eta_{10}}}^2 - 2\,r_{9}\,\cos({\theta_{9}})
1141
\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,{{\eta_{10}}}^2
1142
\\ &&\quad\mbox{} + 4\,r_{9}\,\sin({\theta_{9}})\,m_{10}\,r_{1}\,\cos
1143
({\theta_{1}})\,{{\eta_{1}}}^2 + 4\,r_{9}\,\sin({\theta_{9}})\,m_{10}
1144
\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} + 4\,r
1145
_{9}\,\sin({\theta_{9}})\,m_{10}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4
1146
}}}^2 + 4\,r_{9}\,\sin({\theta_{9}})\,m_{10}\,r_{4}\,\sin({\theta_{4}}
1147
)\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} + 4\,r_{9}\,\sin({\theta_{9}})\,
1148
m_{10}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{9}\,\sin({
1149
\theta_{9}})\,m_{10}\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}}
1150
\\ &&\quad\mbox{} + 4\,r_{9}\,\sin({\theta_{9}})\,m_{10}\,r_{2}\,\cos
1151
({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{9}\,\sin({\theta_{9}})\,m_{10}
1152
\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} + 4\,r
1153
_{9}\,\sin({\theta_{9}})\,m_{10}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5
1154
}}}^2 + 4\,r_{9}\,\sin({\theta_{9}})\,m_{10}\,r_{5}\,\sin({\theta_{5}}
1155
)\,{\dot{\eta}_{5}} \\ &&\quad\mbox{} + 4\,r_{9}\,\sin({\theta_{9}})\,
1156
m_{10}\,r_{8}\,\cos({\theta_{8}})\,{{\eta_{8}}}^2 + 4\,r_{9}\,\sin({
1157
\theta_{9}})\,m_{10}\,r_{8}\,\sin({\theta_{8}})\,{\dot{\eta}_{8}}
1158
\\ &&\quad\mbox{} + 4\,r_{9}\,\sin({\theta_{9}})\,m_{10}\,r_{7}\,\cos
1159
({\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{9}\,\sin({\theta_{9}})\,m_{10}
1160
\,r_{7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}} \\ &&\quad\mbox{} + 4\,r
1161
_{9}\,\sin({\theta_{9}})\,m_{10}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6
1162
}}}^2 + 4\,r_{9}\,\sin({\theta_{9}})\,m_{10}\,r_{6}\,\sin({\theta_{6}}
1163
)\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} - 4\,r_{9}\,\cos({\theta_{9}})\,
1164
m_{10}\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2 + 4\,r_{9}\,\cos({
1165
\theta_{9}})\,m_{10}\,r_{1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1}}
1166
\\ &&\quad\mbox{} - 4\,r_{9}\,\cos({\theta_{9}})\,m_{10}\,r_{3}\,\sin
1167
({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{9}\,\cos({\theta_{9}})\,m_{10}
1168
\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} - 4\,r
1169
_{9}\,\cos({\theta_{9}})\,m_{10}\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2
1170
}}}^2 + 4\,r_{9}\,\cos({\theta_{9}})\,m_{10}\,r_{2}\,\cos({\theta_{2}}
1171
)\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} - 4\,r_{9}\,\cos({\theta_{9}})\,
1172
m_{10}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r_{9}\,\cos({
1173
\theta_{9}})\,m_{10}\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}}
1174
\\ &&\quad\mbox{} - 4\,r_{9}\,\cos({\theta_{9}})\,m_{10}\,r_{5}\,\sin
1175
({\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{9}\,\cos({\theta_{9}})\,m_{10}
1176
\,r_{5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5}} \\ &&\quad\mbox{} - 4\,r
1177
_{9}\,\cos({\theta_{9}})\,m_{10}\,r_{8}\,\sin({\theta_{8}})\,{{\eta_{8
1178
}}}^2 + 4\,r_{9}\,\cos({\theta_{9}})\,m_{10}\,r_{8}\,\cos({\theta_{8}}
1179
)\,{\dot{\eta}_{8}} \\ &&\quad\mbox{} - 4\,r_{9}\,\cos({\theta_{9}})\,
1180
m_{10}\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{9}\,\cos({
1181
\theta_{9}})\,m_{10}\,r_{7}\,\cos({\theta_{7}})\,{\dot{\eta}_{7}}
1182
\\ &&\quad\mbox{} - 4\,r_{9}\,\cos({\theta_{9}})\,m_{10}\,r_{6}\,\sin
1183
({\theta_{6}})\,{{\eta_{6}}}^2 + 4\,r_{9}\,\cos({\theta_{9}})\,m_{10}
1184
\,r_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} + 2\,m
1185
_{9}\,r_{9}\,\sin({\theta_{9}})\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}
1186
}}^2 + 2\,m_{9}\,r_{9}\,\sin({\theta_{9}})\,r_{1}\,\sin({\theta_{1}})
1187
\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} + 2\,m_{9}\,r_{9}\,\sin({\theta_{
1188
9}})\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^2 + 2\,m_{9}\,r_{9}\,
1189
\sin({\theta_{9}})\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}}
1190
\\ &&\quad\mbox{} + 2\,m_{9}\,r_{9}\,\sin({\theta_{9}})\,r_{3}\,\cos(
1191
{\theta_{3}})\,{{\eta_{3}}}^2 + 2\,m_{9}\,r_{9}\,\sin({\theta_{9}})\,r
1192
_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} + 2\,m_{9
1193
}\,r_{9}\,\sin({\theta_{9}})\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^
1194
2 + 2\,m_{9}\,r_{9}\,\sin({\theta_{9}})\,r_{2}\,\sin({\theta_{2}})\,{
1195
\dot{\eta}_{2}} \\ &&\quad\mbox{} + 2\,m_{9}\,r_{9}\,\sin({\theta_{9}}
1196
)\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^2 + 2\,m_{9}\,r_{9}\,\sin({
1197
\theta_{9}})\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}}
1198
\\ &&\quad\mbox{} + 2\,m_{9}\,r_{9}\,\sin({\theta_{9}})\,r_{8}\,\cos(
1199
{\theta_{8}})\,{{\eta_{8}}}^2 + 2\,m_{9}\,r_{9}\,\sin({\theta_{9}})\,r
1200
_{8}\,\sin({\theta_{8}})\,{\dot{\eta}_{8}} \\ &&\quad\mbox{} + 2\,m_{9
1201
}\,r_{9}\,\sin({\theta_{9}})\,r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^
1202
2 + 2\,m_{9}\,r_{9}\,\sin({\theta_{9}})\,r_{7}\,\sin({\theta_{7}})\,{
1203
\dot{\eta}_{7}} \\ &&\quad\mbox{} + 2\,m_{9}\,r_{9}\,\sin({\theta_{9}}
1204
)\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2 + 2\,m_{9}\,r_{9}\,\sin({
1205
\theta_{9}})\,r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}_{6}}
1206
\\ &&\quad\mbox{} - 2\,m_{9}\,r_{9}\,\cos({\theta_{9}})\,r_{1}\,\sin(
1207
{\theta_{1}})\,{{\eta_{1}}}^2 + 2\,m_{9}\,r_{9}\,\cos({\theta_{9}})\,r
1208
_{1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} - 2\,m_{9
1209
}\,r_{9}\,\cos({\theta_{9}})\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^
1210
2 + 2\,m_{9}\,r_{9}\,\cos({\theta_{9}})\,r_{3}\,\cos({\theta_{3}})\,{
1211
\dot{\eta}_{3}} \\ &&\quad\mbox{} - 2\,m_{9}\,r_{9}\,\cos({\theta_{9}}
1212
)\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2 + 2\,m_{9}\,r_{9}\,\cos({
1213
\theta_{9}})\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}}
1214
\\ &&\quad\mbox{} - 2\,m_{9}\,r_{9}\,\cos({\theta_{9}})\,r_{4}\,\sin(
1215
{\theta_{4}})\,{{\eta_{4}}}^2 - 2\,m_{9}\,r_{9}\,\cos({\theta_{9}})\,r
1216
_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 2\,m_{9}
1217
\,r_{9}\,\cos({\theta_{9}})\,r_{5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5
1218
}} - 2\,m_{9}\,r_{9}\,\cos({\theta_{9}})\,r_{8}\,\sin({\theta_{8}})\,{
1219
{\eta_{8}}}^2 \\ &&\quad\mbox{} + 2\,m_{9}\,r_{9}\,\cos({\theta_{9}})
1220
\,r_{8}\,\cos({\theta_{8}})\,{\dot{\eta}_{8}} - 2\,m_{9}\,r_{9}\,\cos(
1221
{\theta_{9}})\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7}}}^2
1222
\\ &&\quad\mbox{} + 2\,m_{9}\,r_{9}\,\cos({\theta_{9}})\,r_{7}\,\cos(
1223
{\theta_{7}})\,{\dot{\eta}_{7}} - 2\,m_{9}\,r_{9}\,\cos({\theta_{9}})
1224
\,r_{6}\,\sin({\theta_{6}})\,{{\eta_{6}}}^2 \\ &&\quad\mbox{} + 2\,m_{
1225
9}\,r_{9}\,\cos({\theta_{9}})\,r_{6}\,\cos({\theta_{6}})\,{\dot{\eta}
1226
_{6}} + 2\,m_{9}\,r_{9}\,\cos({\theta_{9}})\,r_{4}\,\cos({\theta_{4}})
1227
\,{\dot{\eta}_{4}} + 4\,{r_{9}}^2\,m_{10}\,{\dot{\eta}_{9}}
1229
\begin{eqnarray*} && 4\,r_{4}\,\cos({\theta_{4}})\,m_{10}\,r_{8}\,\cos
1230
({\theta_{8}})\,{\dot{\eta}_{8}} - 4\,r_{4}\,\cos({\theta_{4}})\,m_{10
1231
}\,r_{9}\,\sin({\theta_{9}})\,{{\eta_{9}}}^2 \\ &&\quad\mbox{} + 4\,r
1232
_{4}\,\cos({\theta_{4}})\,m_{10}\,r_{9}\,\cos({\theta_{9}})\,{
1233
\dot{\eta}_{9}} - 4\,r_{4}\,\cos({\theta_{4}})\,m_{10}\,r_{7}\,\sin({
1234
\theta_{7}})\,{{\eta_{7}}}^2 \\ &&\quad\mbox{} + 4\,r_{4}\,\cos({
1235
\theta_{4}})\,m_{10}\,r_{7}\,\cos({\theta_{7}})\,{\dot{\eta}_{7}} - 4
1236
\,r_{4}\,\cos({\theta_{4}})\,m_{10}\,r_{6}\,\sin({\theta_{6}})\,{{\eta
1237
_{6}}}^2 \\ &&\quad\mbox{} + 4\,r_{4}\,\cos({\theta_{4}})\,m_{10}\,r_{
1238
6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}} + m_{4}\,g\,r_{4}\,\cos({
1239
\theta_{4}}) + 4\,r_{4}\,\sin({\theta_{4}})\,m_{7}\,r_{5}\,\cos({
1240
\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({
1241
\theta_{4}})\,m_{7}\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}} + 4\,
1242
r_{4}\,\sin({\theta_{4}})\,m_{7}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6
1243
}}}^2 \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{7}\,r_{6}\,
1244
\sin({\theta_{6}})\,{\dot{\eta}_{6}} - 4\,r_{4}\,\cos({\theta_{4}})\,m
1245
_{9}\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4
1246
\,r_{4}\,\cos({\theta_{4}})\,m_{9}\,r_{2}\,\cos({\theta_{2}})\,{
1247
\dot{\eta}_{2}} + 4\,r_{4}\,\cos({\theta_{4}})\,m_{9}\,r_{1}\,\cos({
1248
\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} - 4\,r_{4}\,\cos({
1249
\theta_{4}})\,m_{9}\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2 + 2\,m
1250
_{4}\,r_{4}\,\sin({\theta_{4}})\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}
1251
}}^2 \\ &&\quad\mbox{} + 2\,m_{4}\,r_{4}\,\sin({\theta_{4}})\,r_{2}\,
1252
\sin({\theta_{2}})\,{\dot{\eta}_{2}} - 2\,m_{4}\,r_{4}\,\cos({\theta_{
1253
4}})\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} - 4
1254
\,r_{4}\,\cos({\theta_{4}})\,m_{6}\,r_{1}\,\sin({\theta_{1}})\,{{\eta
1255
_{1}}}^2 + 4\,r_{4}\,\cos({\theta_{4}})\,m_{6}\,r_{1}\,\cos({\theta_{1
1256
}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} - 4\,r_{4}\,\cos({\theta_{4}})
1257
\,m_{6}\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{4}\,\sin({
1258
\theta_{4}})\,m_{7}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2
1259
\\ &&\quad\mbox{} + 2\,m_{4}\,r_{4}\,\cos({\theta_{4}})\,r_{2}\,\cos(
1260
{\theta_{2}})\,{\dot{\eta}_{2}} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{7}
1261
\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} + 4\,r
1262
_{4}\,\sin({\theta_{4}})\,m_{7}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}
1263
}}^2 + 4\,r_{4}\,\sin({\theta_{4}})\,m_{7}\,r_{3}\,\sin({\theta_{3}})
1264
\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m
1265
_{7}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 - 2\,m_{4}\,r_{4}\,
1266
\cos({\theta_{4}})\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2
1267
\\ &&\quad\mbox{} + 2\,m_{4}\,r_{4}\,\cos({\theta_{4}})\,r_{1}\,\cos(
1268
{\theta_{1}})\,{\dot{\eta}_{1}} - 2\,m_{4}\,r_{4}\,\cos({\theta_{4}})
1269
\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} + 4\,r_{
1270
4}\,\sin({\theta_{4}})\,m_{7}\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}
1271
_{2}} + 4\,r_{4}\,\cos({\theta_{4}})\,m_{6}\,r_{3}\,\cos({\theta_{3}})
1272
\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} - 4\,r_{4}\,\cos({\theta_{4}})\,m
1273
_{6}\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{4}\,\cos({
1274
\theta_{4}})\,m_{6}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}}
1275
\\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{9}\,r_{1}\,\sin(
1276
{\theta_{1}})\,{\dot{\eta}_{1}} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{9}
1277
\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} + 4\,r
1278
_{4}\,\sin({\theta_{4}})\,m_{9}\,r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}
1279
}}^2 + 4\,r_{4}\,\sin({\theta_{4}})\,m_{9}\,r_{7}\,\sin({\theta_{7}})
1280
\,{\dot{\eta}_{7}} \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m
1281
_{9}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2 + 4\,r_{4}\,\sin({
1282
\theta_{4}})\,m_{9}\,r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}_{6}}
1283
\\ &&\quad\mbox{} - 4\,r_{4}\,\cos({\theta_{4}})\,m_{9}\,r_{7}\,\sin(
1284
{\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{4}\,\cos({\theta_{4}})\,m_{9}\,r
1285
_{7}\,\cos({\theta_{7}})\,{\dot{\eta}_{7}} \\ &&\quad\mbox{} - 4\,r_{4
1286
}\,\cos({\theta_{4}})\,m_{9}\,r_{6}\,\sin({\theta_{6}})\,{{\eta_{6}}}^
1287
2 + 4\,r_{4}\,\cos({\theta_{4}})\,m_{9}\,r_{6}\,\cos({\theta_{6}})\,{
1288
\dot{\eta}_{6}} \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{8
1289
}\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}} + 4\,r_{4}\,\sin({
1290
\theta_{4}})\,m_{8}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^2
1291
\\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{8}\,r_{5}\,\sin(
1292
{\theta_{5}})\,{\dot{\eta}_{5}} - 4\,r_{4}\,\cos({\theta_{4}})\,m_{7}
1293
\,r_{6}\,\sin({\theta_{6}})\,{{\eta_{6}}}^2 \\ &&\quad\mbox{} + 4\,r_{
1294
4}\,\cos({\theta_{4}})\,m_{7}\,r_{6}\,\cos({\theta_{6}})\,{\dot{\eta}
1295
_{6}} + 4\,r_{4}\,\cos({\theta_{4}})\,m_{7}\,r_{5}\,\cos({\theta_{5}})
1296
\,{\dot{\eta}_{5}} \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m
1297
_{10}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2 + 4\,r_{4}\,\cos({
1298
\theta_{4}})\,m_{8}\,r_{7}\,\cos({\theta_{7}})\,{\dot{\eta}_{7}}
1299
\\ &&\quad\mbox{} - 4\,r_{4}\,\cos({\theta_{4}})\,m_{8}\,r_{6}\,\sin(
1300
{\theta_{6}})\,{{\eta_{6}}}^2 - 4\,r_{4}\,\cos({\theta_{4}})\,m_{8}\,r
1301
_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{4}
1302
\,\cos({\theta_{4}})\,m_{8}\,r_{1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1
1303
}} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{9}\,r_{5}\,\cos({\theta_{5}})\,{
1304
{\eta_{5}}}^2 \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{9}
1305
\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}} + 4\,r_{4}\,\sin({\theta
1306
_{4}})\,m_{9}\,r_{8}\,\cos({\theta_{8}})\,{{\eta_{8}}}^2
1307
\\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{9}\,r_{8}\,\sin(
1308
{\theta_{8}})\,{\dot{\eta}_{8}} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{9}
1309
\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} + 4\,r_{
1310
4}\,\sin({\theta_{4}})\,m_{9}\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}
1311
_{3}} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{9}\,r_{2}\,\cos({\theta_{2}})
1312
\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{
1313
8}\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}} + 4\,r_{4}\,\sin({
1314
\theta_{4}})\,m_{8}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2
1315
\\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{8}\,r_{1}\,\cos(
1316
{\theta_{1}})\,{{\eta_{1}}}^2 + 4\,r_{4}\,\cos({\theta_{4}})\,m_{8}\,r
1317
_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} + 4\,r_{4
1318
}\,\sin({\theta_{4}})\,m_{8}\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{
1319
1}} + 4\,r_{4}\,\cos({\theta_{4}})\,m_{8}\,r_{3}\,\cos({\theta_{3}})\,
1320
{\dot{\eta}_{3}} \\ &&\quad\mbox{} - 4\,r_{4}\,\cos({\theta_{4}})\,m_{
1321
8}\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{4}\,\cos({\theta
1322
_{4}})\,m_{8}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}}
1323
\\ &&\quad\mbox{} - 4\,r_{4}\,\cos({\theta_{4}})\,m_{8}\,r_{3}\,\sin(
1324
{\theta_{3}})\,{{\eta_{3}}}^2 - 4\,r_{4}\,\cos({\theta_{4}})\,m_{8}\,r
1325
_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 4\,r_{4}
1326
\,\cos({\theta_{4}})\,m_{8}\,r_{5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5
1327
}} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{6}\,r_{2}\,\sin({\theta_{2}})\,{
1328
\dot{\eta}_{2}} \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{6
1329
}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2 + 4\,r_{4}\,\sin({\theta
1330
_{4}})\,m_{6}\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}}
1331
\\ &&\quad\mbox{} + 4\,r_{4}\,\cos({\theta_{4}})\,m_{6}\,r_{5}\,\cos(
1332
{\theta_{5}})\,{\dot{\eta}_{5}} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{6}
1333
\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} + 4\,r_{
1334
4}\,\sin({\theta_{4}})\,m_{6}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}
1335
^2 + 4\,r_{4}\,\sin({\theta_{4}})\,m_{5}\,r_{1}\,\cos({\theta_{1}})\,{
1336
{\eta_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{5}
1337
\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{4}\,\sin({\theta_{
1338
4}})\,m_{5}\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}}
1339
\\ &&\quad\mbox{} - 4\,r_{4}\,\cos({\theta_{4}})\,m_{5}\,r_{2}\,\sin(
1340
{\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{4}\,\cos({\theta_{4}})\,m_{5}\,r
1341
_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} + 2\,m_{4
1342
}\,r_{4}\,\sin({\theta_{4}})\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^
1343
2 + 2\,m_{4}\,r_{4}\,\sin({\theta_{4}})\,r_{1}\,\sin({\theta_{1}})\,{
1344
\dot{\eta}_{1}} \\ &&\quad\mbox{} + 2\,m_{4}\,r_{4}\,\sin({\theta_{4}}
1345
)\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{4}\,\sin({\theta
1346
_{4}})\,m_{5}\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}}
1347
\\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{5}\,r_{3}\,\cos(
1348
{\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{4}\,\sin({\theta_{4}})\,m_{5}\,r
1349
_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,r_{4
1350
}\,\sin({\theta_{4}})\,m_{6}\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{
1351
5}} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{6}\,r_{3}\,\sin({\theta_{3}})\,
1352
{\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,r_{4}\,\cos({\theta_{4}})\,m_{
1353
10}\,r_{5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5}} + 4\,r_{4}\,\sin({
1354
\theta_{4}})\,m_{10}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^2
1355
\\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{10}\,r_{5}\,\sin
1356
({\theta_{5}})\,{\dot{\eta}_{5}} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{10
1357
}\,r_{9}\,\cos({\theta_{9}})\,{{\eta_{9}}}^2 \\ &&\quad\mbox{} + 4\,r
1358
_{4}\,\sin({\theta_{4}})\,m_{10}\,r_{9}\,\sin({\theta_{9}})\,{
1359
\dot{\eta}_{9}} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{10}\,r_{8}\,\cos({
1360
\theta_{8}})\,{{\eta_{8}}}^2 \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({
1361
\theta_{4}})\,m_{10}\,r_{8}\,\sin({\theta_{8}})\,{\dot{\eta}_{8}} - 4
1362
\,r_{4}\,\cos({\theta_{4}})\,m_{7}\,r_{3}\,\sin({\theta_{3}})\,{{\eta
1363
_{3}}}^2 \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{10}\,r_{
1364
7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}} + 4\,r_{4}\,\sin({\theta_{4}}
1365
)\,m_{10}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2 \\ &&\quad\mbox{}
1366
+ 4\,r_{4}\,\sin({\theta_{4}})\,m_{10}\,r_{6}\,\sin({\theta_{6}})\,{
1367
\dot{\eta}_{6}} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{8}\,r_{7}\,\cos({
1368
\theta_{7}})\,{{\eta_{7}}}^2 \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({
1369
\theta_{4}})\,m_{8}\,r_{7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}} + 4\,
1370
r_{4}\,\sin({\theta_{4}})\,m_{8}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6
1371
}}}^2 \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{8}\,r_{6}\,
1372
\sin({\theta_{6}})\,{\dot{\eta}_{6}} + 4\,r_{4}\,\sin({\theta_{4}})\,m
1373
_{10}\,r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^2 \\ &&\quad\mbox{} - 4
1374
\,r_{4}\,\cos({\theta_{4}})\,m_{10}\,r_{1}\,\sin({\theta_{1}})\,{{\eta
1375
_{1}}}^2 + 4\,r_{4}\,\cos({\theta_{4}})\,m_{10}\,r_{1}\,\cos({\theta_{
1376
1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} - 4\,r_{4}\,\cos({\theta_{4}}
1377
)\,m_{10}\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{4}\,\cos(
1378
{\theta_{4}})\,m_{10}\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}}
1379
\\ &&\quad\mbox{} - 4\,r_{4}\,\cos({\theta_{4}})\,m_{10}\,r_{2}\,\sin
1380
({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{4}\,\cos({\theta_{4}})\,m_{10}
1381
\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} + 4\,r
1382
_{4}\,\sin({\theta_{4}})\,m_{10}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3
1383
}}}^2 + 4\,r_{4}\,\sin({\theta_{4}})\,m_{10}\,r_{3}\,\sin({\theta_{3}}
1384
)\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,
1385
m_{10}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{4}\,\sin({
1386
\theta_{4}})\,m_{10}\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}}
1387
\\ &&\quad\mbox{} + 4\,r_{4}\,\cos({\theta_{4}})\,m_{7}\,r_{3}\,\cos(
1388
{\theta_{3}})\,{\dot{\eta}_{3}} - 4\,r_{4}\,\cos({\theta_{4}})\,m_{7}
1389
\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{
1390
4}\,\cos({\theta_{4}})\,m_{7}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}
1391
_{2}} - 4\,r_{4}\,\cos({\theta_{4}})\,m_{7}\,r_{5}\,\sin({\theta_{5}})
1392
\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} - 4\,r_{4}\,\cos({\theta_{4}})\,m_{
1393
7}\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2 + 2\,r_{4}\,\cos({\theta
1394
_{4}})\,m_{8}\,g + 2\,r_{4}\,\cos({\theta_{4}})\,m_{10}\,g + 2\,r_{4}
1395
\,\cos({\theta_{4}})\,m_{7}\,g \\ &&\quad\mbox{} + 2\,r_{4}\,\cos({
1396
\theta_{4}})\,m_{9}\,g + 2\,r_{4}\,\cos({\theta_{4}})\,m_{5}\,g + 2\,r
1397
_{4}\,\cos({\theta_{4}})\,m_{6}\,g - 4\,r_{4}\,\cos({\theta_{4}})\,m_{
1398
10}\,r_{8}\,\sin({\theta_{8}})\,{{\eta_{8}}}^2 \\ &&\quad\mbox{} + 2\,
1399
m_{4}\,r_{4}\,\cos({\theta_{4}})\,r_{3}\,\cos({\theta_{3}})\,{
1400
\dot{\eta}_{3}} - 4\,r_{4}\,\cos({\theta_{4}})\,m_{6}\,r_{3}\,\sin({
1401
\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} - 4\,r_{4}\,\cos({
1402
\theta_{4}})\,m_{9}\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2 - 4\,r
1403
_{4}\,\cos({\theta_{4}})\,m_{5}\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}
1404
}}^2 \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{6}\,r_{2}\,
1405
\cos({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{4}\,\sin({\theta_{4}})\,m_{
1406
8}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} - 4\,r
1407
_{4}\,\cos({\theta_{4}})\,m_{8}\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7}
1408
}}^2 + 4\,r_{4}\,\sin({\theta_{4}})\,m_{9}\,r_{1}\,\cos({\theta_{1}})
1409
\,{{\eta_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{4}\,\sin({\theta_{4}})\,m_{
1410
10}\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} + 4\,r_{4}\,\cos({
1411
\theta_{4}})\,m_{7}\,r_{1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1}}
1412
\\ &&\quad\mbox{} - 4\,r_{4}\,\cos({\theta_{4}})\,m_{10}\,r_{5}\,\sin
1413
({\theta_{5}})\,{{\eta_{5}}}^2 + J_{4}\,{\dot{\eta}_{4}} + 2\,r_{4}\,
1414
\cos({\theta_{4}})\,m_{8}\,r_{8}\,\cos({\theta_{8}})\,{\dot{\eta}_{8}}
1415
\\ &&\quad\mbox{} + 2\,r_{4}\,\sin({\theta_{4}})\,m_{8}\,r_{8}\,\sin(
1416
{\theta_{8}})\,{\dot{\eta}_{8}} + 2\,r_{4}\,\sin({\theta_{4}})\,m_{9}
1417
\,r_{9}\,\sin({\theta_{9}})\,{\dot{\eta}_{9}} \\ &&\quad\mbox{} + 2\,r
1418
_{4}\,\cos({\theta_{4}})\,m_{9}\,r_{9}\,\cos({\theta_{9}})\,{
1419
\dot{\eta}_{9}} + 2\,r_{4}\,\sin({\theta_{4}})\,m_{10}\,r_{10}\,\sin({
1420
\theta_{10}})\,{\dot{\eta}_{10}} \\ &&\quad\mbox{} + 2\,r_{4}\,\cos({
1421
\theta_{4}})\,m_{10}\,r_{10}\,\cos({\theta_{10}})\,{\dot{\eta}_{10}}
1422
+ 2\,m_{4}\,r_{4}\,\sin({\theta_{4}})\,r_{3}\,\sin({\theta_{3}})\,{
1423
\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,r_{4}\,\cos({\theta_{4}})\,m_{9
1424
}\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}} - 4\,r_{4}\,\cos({
1425
\theta_{4}})\,m_{9}\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2
1426
\\ &&\quad\mbox{} + 4\,r_{4}\,\cos({\theta_{4}})\,m_{9}\,r_{5}\,\cos(
1427
{\theta_{5}})\,{\dot{\eta}_{5}} - 4\,r_{4}\,\cos({\theta_{4}})\,m_{9}
1428
\,r_{8}\,\sin({\theta_{8}})\,{{\eta_{8}}}^2 \\ &&\quad\mbox{} + 4\,r_{
1429
4}\,\cos({\theta_{4}})\,m_{9}\,r_{8}\,\cos({\theta_{8}})\,{\dot{\eta}
1430
_{8}} + 4\,r_{4}\,\cos({\theta_{4}})\,m_{5}\,r_{1}\,\cos({\theta_{1}})
1431
\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} - 4\,r_{4}\,\cos({\theta_{4}})\,m
1432
_{5}\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{4}\,\cos({
1433
\theta_{4}})\,m_{5}\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}}
1434
\\ &&\quad\mbox{} + 2\,r_{4}\,\sin({\theta_{4}})\,m_{5}\,r_{5}\,\cos(
1435
{\theta_{5}})\,{{\eta_{5}}}^2 - 2\,r_{4}\,\cos({\theta_{4}})\,m_{5}\,r
1436
_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 2\,r_{4}
1437
\,\sin({\theta_{4}})\,m_{6}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2
1438
- 2\,r_{4}\,\cos({\theta_{4}})\,m_{6}\,r_{6}\,\sin({\theta_{6}})\,{{
1439
\eta_{6}}}^2 \\ &&\quad\mbox{} + 2\,r_{4}\,\sin({\theta_{4}})\,m_{7}\,
1440
r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^2 - 2\,r_{4}\,\cos({\theta_{4}
1441
})\,m_{7}\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7}}}^2 \\ &&\quad\mbox{}
1442
- 2\,r_{4}\,\cos({\theta_{4}})\,m_{8}\,r_{8}\,\sin({\theta_{8}})\,{{
1443
\eta_{8}}}^2 + 2\,r_{4}\,\sin({\theta_{4}})\,m_{8}\,r_{8}\,\cos({
1444
\theta_{8}})\,{{\eta_{8}}}^2 \\ &&\quad\mbox{} + 2\,r_{4}\,\sin({
1445
\theta_{4}})\,m_{9}\,r_{9}\,\cos({\theta_{9}})\,{{\eta_{9}}}^2 - 2\,r
1446
_{4}\,\cos({\theta_{4}})\,m_{9}\,r_{9}\,\sin({\theta_{9}})\,{{\eta_{9}
1447
}}^2 \\ &&\quad\mbox{} + 2\,r_{4}\,\sin({\theta_{4}})\,m_{10}\,r_{10}
1448
\,\cos({\theta_{10}})\,{{\eta_{10}}}^2 - 2\,r_{4}\,\cos({\theta_{4}})
1449
\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,{{\eta_{10}}}^2 + 4\,{r_{4}}^2
1450
\,m_{6}\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} + 4\,{r_{4}}^2\,m_{9}\,{
1451
\dot{\eta}_{4}} + 4\,{r_{4}}^2\,m_{10}\,{\dot{\eta}_{4}} + 4\,{r_{4}}^
1452
2\,m_{7}\,{\dot{\eta}_{4}} + 4\,{r_{4}}^2\,m_{8}\,{\dot{\eta}_{4}} + 4
1453
\,{r_{4}}^2\,m_{5}\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} + m_{4}\,{r_{4}
1454
}^2\,{\dot{\eta}_{4}} + 2\,r_{4}\,\sin({\theta_{4}})\,m_{5}\,r_{5}\,
1455
\sin({\theta_{5}})\,{\dot{\eta}_{5}} + 2\,r_{4}\,\cos({\theta_{4}})\,m
1456
_{5}\,r_{5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5}} \\ &&\quad\mbox{} +
1457
2\,r_{4}\,\cos({\theta_{4}})\,m_{6}\,r_{6}\,\cos({\theta_{6}})\,{
1458
\dot{\eta}_{6}} + 2\,r_{4}\,\sin({\theta_{4}})\,m_{6}\,r_{6}\,\sin({
1459
\theta_{6}})\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} + 2\,r_{4}\,\sin({
1460
\theta_{4}})\,m_{7}\,r_{7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}} + 2\,
1461
r_{4}\,\cos({\theta_{4}})\,m_{7}\,r_{7}\,\cos({\theta_{7}})\,{
1462
\dot{\eta}_{7}} \end{eqnarray*}
1463
\begin{eqnarray*} && m_{7}\,g\,r_{7}\,\cos({\theta_{7}}) + 4\,{r_{7}}^
1464
2\,m_{8}\,{\dot{\eta}_{7}} + 4\,{r_{7}}^2\,m_{9}\,{\dot{\eta}_{7}} + 4
1465
\,{r_{7}}^2\,m_{10}\,{\dot{\eta}_{7}} + 2\,r_{7}\,\cos({\theta_{7}})\,
1466
m_{9}\,g \\ &&\quad\mbox{} + 2\,r_{7}\,\cos({\theta_{7}})\,m_{10}\,g
1467
+ 2\,r_{7}\,\cos({\theta_{7}})\,m_{8}\,g + J_{7}\,{\dot{\eta}_{7}} +
1468
2\,r_{7}\,\sin({\theta_{7}})\,m_{8}\,r_{8}\,\sin({\theta_{8}})\,{
1469
\dot{\eta}_{8}} \\ &&\quad\mbox{} + 2\,r_{7}\,\cos({\theta_{7}})\,m_{8
1470
}\,r_{8}\,\cos({\theta_{8}})\,{\dot{\eta}_{8}} + 2\,r_{7}\,\sin({
1471
\theta_{7}})\,m_{9}\,r_{9}\,\sin({\theta_{9}})\,{\dot{\eta}_{9}}
1472
\\ &&\quad\mbox{} + 2\,r_{7}\,\cos({\theta_{7}})\,m_{9}\,r_{9}\,\cos(
1473
{\theta_{9}})\,{\dot{\eta}_{9}} + 2\,r_{7}\,\sin({\theta_{7}})\,m_{10}
1474
\,r_{10}\,\sin({\theta_{10}})\,{\dot{\eta}_{10}} \\ &&\quad\mbox{} + 2
1475
\,r_{7}\,\cos({\theta_{7}})\,m_{10}\,r_{10}\,\cos({\theta_{10}})\,{
1476
\dot{\eta}_{10}} + 2\,r_{7}\,\sin({\theta_{7}})\,m_{8}\,r_{8}\,\cos({
1477
\theta_{8}})\,{{\eta_{8}}}^2 \\ &&\quad\mbox{} - 2\,r_{7}\,\cos({
1478
\theta_{7}})\,m_{8}\,r_{8}\,\sin({\theta_{8}})\,{{\eta_{8}}}^2 + 2\,r
1479
_{7}\,\sin({\theta_{7}})\,m_{9}\,r_{9}\,\cos({\theta_{9}})\,{{\eta_{9}
1480
}}^2 \\ &&\quad\mbox{} - 2\,r_{7}\,\cos({\theta_{7}})\,m_{9}\,r_{9}\,
1481
\sin({\theta_{9}})\,{{\eta_{9}}}^2 + 2\,r_{7}\,\sin({\theta_{7}})\,m_{
1482
10}\,r_{10}\,\cos({\theta_{10}})\,{{\eta_{10}}}^2 \\ &&\quad\mbox{} -
1483
2\,r_{7}\,\cos({\theta_{7}})\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,{{
1484
\eta_{10}}}^2 + m_{7}\,{r_{7}}^2\,{\dot{\eta}_{7}} + 4\,r_{7}\,\sin({
1485
\theta_{7}})\,m_{10}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2
1486
\\ &&\quad\mbox{} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{10}\,r_{1}\,\sin
1487
({\theta_{1}})\,{\dot{\eta}_{1}} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{8}
1488
\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{
1489
7}\,\sin({\theta_{7}})\,m_{8}\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}
1490
_{1}} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{8}\,r_{4}\,\cos({\theta_{4}})
1491
\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{
1492
8}\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}} + 4\,r_{7}\,\sin({
1493
\theta_{7}})\,m_{8}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2
1494
\\ &&\quad\mbox{} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{8}\,r_{3}\,\sin(
1495
{\theta_{3}})\,{\dot{\eta}_{3}} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{8}
1496
\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{
1497
7}\,\sin({\theta_{7}})\,m_{8}\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}
1498
_{2}} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{8}\,r_{5}\,\cos({\theta_{5}})
1499
\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{
1500
8}\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}} + 4\,r_{7}\,\sin({
1501
\theta_{7}})\,m_{8}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2
1502
\\ &&\quad\mbox{} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{8}\,r_{6}\,\sin(
1503
{\theta_{6}})\,{\dot{\eta}_{6}} - 4\,r_{7}\,\cos({\theta_{7}})\,m_{8}
1504
\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{
1505
7}\,\cos({\theta_{7}})\,m_{8}\,r_{1}\,\cos({\theta_{1}})\,{\dot{\eta}
1506
_{1}} - 4\,r_{7}\,\cos({\theta_{7}})\,m_{8}\,r_{3}\,\sin({\theta_{3}})
1507
\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} + 4\,r_{7}\,\cos({\theta_{7}})\,m_{
1508
8}\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}} - 4\,r_{7}\,\cos({
1509
\theta_{7}})\,m_{8}\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2
1510
\\ &&\quad\mbox{} + 4\,r_{7}\,\cos({\theta_{7}})\,m_{8}\,r_{2}\,\cos(
1511
{\theta_{2}})\,{\dot{\eta}_{2}} - 4\,r_{7}\,\cos({\theta_{7}})\,m_{8}
1512
\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{
1513
7}\,\cos({\theta_{7}})\,m_{8}\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}
1514
_{4}} - 4\,r_{7}\,\cos({\theta_{7}})\,m_{8}\,r_{5}\,\sin({\theta_{5}})
1515
\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 4\,r_{7}\,\cos({\theta_{7}})\,m_{
1516
8}\,r_{5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5}} - 4\,r_{7}\,\cos({
1517
\theta_{7}})\,m_{8}\,r_{6}\,\sin({\theta_{6}})\,{{\eta_{6}}}^2
1518
\\ &&\quad\mbox{} + 4\,r_{7}\,\cos({\theta_{7}})\,m_{8}\,r_{6}\,\cos(
1519
{\theta_{6}})\,{\dot{\eta}_{6}} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{9}
1520
\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{
1521
7}\,\sin({\theta_{7}})\,m_{9}\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}
1522
_{1}} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{9}\,r_{4}\,\cos({\theta_{4}})
1523
\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{
1524
9}\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}} + 4\,r_{7}\,\sin({
1525
\theta_{7}})\,m_{9}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2
1526
\\ &&\quad\mbox{} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{9}\,r_{3}\,\sin(
1527
{\theta_{3}})\,{\dot{\eta}_{3}} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{9}
1528
\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{
1529
7}\,\sin({\theta_{7}})\,m_{9}\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}
1530
_{2}} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{9}\,r_{5}\,\cos({\theta_{5}})
1531
\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{
1532
9}\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}} + 4\,r_{7}\,\sin({
1533
\theta_{7}})\,m_{9}\,r_{8}\,\cos({\theta_{8}})\,{{\eta_{8}}}^2
1534
\\ &&\quad\mbox{} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{9}\,r_{8}\,\sin(
1535
{\theta_{8}})\,{\dot{\eta}_{8}} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{9}
1536
\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2 \\ &&\quad\mbox{} + 4\,r_{
1537
7}\,\sin({\theta_{7}})\,m_{9}\,r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}
1538
_{6}} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{10}\,r_{4}\,\cos({\theta_{4}}
1539
)\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{7}\,\sin({\theta_{7}})\,m
1540
_{10}\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}} + 4\,r_{7}\,\sin({
1541
\theta_{7}})\,m_{10}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2
1542
\\ &&\quad\mbox{} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{10}\,r_{3}\,\sin
1543
({\theta_{3}})\,{\dot{\eta}_{3}} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{10
1544
}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r
1545
_{7}\,\sin({\theta_{7}})\,m_{10}\,r_{2}\,\sin({\theta_{2}})\,{
1546
\dot{\eta}_{2}} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{10}\,r_{5}\,\cos({
1547
\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 4\,r_{7}\,\sin({
1548
\theta_{7}})\,m_{10}\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}} + 4
1549
\,r_{7}\,\sin({\theta_{7}})\,m_{10}\,r_{9}\,\cos({\theta_{9}})\,{{\eta
1550
_{9}}}^2 \\ &&\quad\mbox{} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{10}\,r_{
1551
9}\,\sin({\theta_{9}})\,{\dot{\eta}_{9}} + 4\,r_{7}\,\sin({\theta_{7}}
1552
)\,m_{10}\,r_{8}\,\cos({\theta_{8}})\,{{\eta_{8}}}^2 \\ &&\quad\mbox{}
1553
+ 4\,r_{7}\,\sin({\theta_{7}})\,m_{10}\,r_{8}\,\sin({\theta_{8}})\,{
1554
\dot{\eta}_{8}} + 4\,r_{7}\,\sin({\theta_{7}})\,m_{10}\,r_{6}\,\cos({
1555
\theta_{6}})\,{{\eta_{6}}}^2 \\ &&\quad\mbox{} + 4\,r_{7}\,\sin({
1556
\theta_{7}})\,m_{10}\,r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}_{6}} - 4
1557
\,r_{7}\,\cos({\theta_{7}})\,m_{10}\,r_{1}\,\sin({\theta_{1}})\,{{\eta
1558
_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{7}\,\cos({\theta_{7}})\,m_{10}\,r_{
1559
1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1}} - 4\,r_{7}\,\cos({\theta_{7}}
1560
)\,m_{10}\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{}
1561
+ 4\,r_{7}\,\cos({\theta_{7}})\,m_{10}\,r_{3}\,\cos({\theta_{3}})\,{
1562
\dot{\eta}_{3}} - 4\,r_{7}\,\cos({\theta_{7}})\,m_{10}\,r_{2}\,\sin({
1563
\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{7}\,\cos({
1564
\theta_{7}})\,m_{10}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}} - 4
1565
\,r_{7}\,\cos({\theta_{7}})\,m_{10}\,r_{4}\,\sin({\theta_{4}})\,{{\eta
1566
_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{7}\,\cos({\theta_{7}})\,m_{10}\,r_{
1567
4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}} - 4\,r_{7}\,\cos({\theta_{7}}
1568
)\,m_{10}\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{}
1569
+ 4\,r_{7}\,\cos({\theta_{7}})\,m_{10}\,r_{5}\,\cos({\theta_{5}})\,{
1570
\dot{\eta}_{5}} - 4\,r_{7}\,\cos({\theta_{7}})\,m_{10}\,r_{8}\,\sin({
1571
\theta_{8}})\,{{\eta_{8}}}^2 \\ &&\quad\mbox{} + 4\,r_{7}\,\cos({
1572
\theta_{7}})\,m_{10}\,r_{8}\,\cos({\theta_{8}})\,{\dot{\eta}_{8}} - 4
1573
\,r_{7}\,\cos({\theta_{7}})\,m_{10}\,r_{9}\,\sin({\theta_{9}})\,{{\eta
1574
_{9}}}^2 \\ &&\quad\mbox{} + 4\,r_{7}\,\cos({\theta_{7}})\,m_{10}\,r_{
1575
9}\,\cos({\theta_{9}})\,{\dot{\eta}_{9}} - 4\,r_{7}\,\cos({\theta_{7}}
1576
)\,m_{10}\,r_{6}\,\sin({\theta_{6}})\,{{\eta_{6}}}^2 \\ &&\quad\mbox{}
1577
+ 4\,r_{7}\,\cos({\theta_{7}})\,m_{10}\,r_{6}\,\cos({\theta_{6}})\,{
1578
\dot{\eta}_{6}} + 2\,m_{7}\,r_{7}\,\sin({\theta_{7}})\,r_{1}\,\cos({
1579
\theta_{1}})\,{{\eta_{1}}}^2 \\ &&\quad\mbox{} + 2\,m_{7}\,r_{7}\,\sin
1580
({\theta_{7}})\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} + 2\,m_{7}
1581
\,r_{7}\,\sin({\theta_{7}})\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^2
1582
\\ &&\quad\mbox{} + 2\,m_{7}\,r_{7}\,\sin({\theta_{7}})\,r_{4}\,\sin(
1583
{\theta_{4}})\,{\dot{\eta}_{4}} + 2\,m_{7}\,r_{7}\,\sin({\theta_{7}})
1584
\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} + 2\,m_{
1585
7}\,r_{7}\,\sin({\theta_{7}})\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}
1586
_{3}} + 2\,m_{7}\,r_{7}\,\sin({\theta_{7}})\,r_{2}\,\cos({\theta_{2}})
1587
\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 2\,m_{7}\,r_{7}\,\sin({\theta_{7}
1588
})\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}} + 2\,m_{7}\,r_{7}\,
1589
\sin({\theta_{7}})\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^2
1590
\\ &&\quad\mbox{} + 2\,m_{7}\,r_{7}\,\sin({\theta_{7}})\,r_{5}\,\sin(
1591
{\theta_{5}})\,{\dot{\eta}_{5}} + 2\,m_{7}\,r_{7}\,\sin({\theta_{7}})
1592
\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2 \\ &&\quad\mbox{} + 2\,m_{
1593
7}\,r_{7}\,\sin({\theta_{7}})\,r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}
1594
_{6}} - 4\,r_{7}\,\cos({\theta_{7}})\,m_{9}\,r_{1}\,\sin({\theta_{1}})
1595
\,{{\eta_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{7}\,\cos({\theta_{7}})\,m_{
1596
9}\,r_{1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1}} - 4\,r_{7}\,\cos({
1597
\theta_{7}})\,m_{9}\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2
1598
\\ &&\quad\mbox{} + 4\,r_{7}\,\cos({\theta_{7}})\,m_{9}\,r_{3}\,\cos(
1599
{\theta_{3}})\,{\dot{\eta}_{3}} - 4\,r_{7}\,\cos({\theta_{7}})\,m_{9}
1600
\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{
1601
7}\,\cos({\theta_{7}})\,m_{9}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}
1602
_{2}} - 4\,r_{7}\,\cos({\theta_{7}})\,m_{9}\,r_{4}\,\sin({\theta_{4}})
1603
\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{7}\,\cos({\theta_{7}})\,m_{
1604
9}\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}} - 4\,r_{7}\,\cos({
1605
\theta_{7}})\,m_{9}\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2
1606
\\ &&\quad\mbox{} + 4\,r_{7}\,\cos({\theta_{7}})\,m_{9}\,r_{5}\,\cos(
1607
{\theta_{5}})\,{\dot{\eta}_{5}} - 4\,r_{7}\,\cos({\theta_{7}})\,m_{9}
1608
\,r_{8}\,\sin({\theta_{8}})\,{{\eta_{8}}}^2 \\ &&\quad\mbox{} + 4\,r_{
1609
7}\,\cos({\theta_{7}})\,m_{9}\,r_{8}\,\cos({\theta_{8}})\,{\dot{\eta}
1610
_{8}} - 4\,r_{7}\,\cos({\theta_{7}})\,m_{9}\,r_{6}\,\sin({\theta_{6}})
1611
\,{{\eta_{6}}}^2 \\ &&\quad\mbox{} + 4\,r_{7}\,\cos({\theta_{7}})\,m_{
1612
9}\,r_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}} - 2\,m_{7}\,r_{7}\,
1613
\cos({\theta_{7}})\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2
1614
\\ &&\quad\mbox{} + 2\,m_{7}\,r_{7}\,\cos({\theta_{7}})\,r_{1}\,\cos(
1615
{\theta_{1}})\,{\dot{\eta}_{1}} - 2\,m_{7}\,r_{7}\,\cos({\theta_{7}})
1616
\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} + 2\,m_{
1617
7}\,r_{7}\,\cos({\theta_{7}})\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}
1618
_{3}} - 2\,m_{7}\,r_{7}\,\cos({\theta_{7}})\,r_{2}\,\sin({\theta_{2}})
1619
\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 2\,m_{7}\,r_{7}\,\cos({\theta_{7}
1620
})\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}} - 2\,m_{7}\,r_{7}\,
1621
\cos({\theta_{7}})\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^2
1622
\\ &&\quad\mbox{} + 2\,m_{7}\,r_{7}\,\cos({\theta_{7}})\,r_{4}\,\cos(
1623
{\theta_{4}})\,{\dot{\eta}_{4}} - 2\,m_{7}\,r_{7}\,\cos({\theta_{7}})
1624
\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 2\,m_{
1625
7}\,r_{7}\,\cos({\theta_{7}})\,r_{5}\,\cos({\theta_{5}})\,{\dot{\eta}
1626
_{5}} - 2\,m_{7}\,r_{7}\,\cos({\theta_{7}})\,r_{6}\,\sin({\theta_{6}})
1627
\,{{\eta_{6}}}^2 \\ &&\quad\mbox{} + 2\,m_{7}\,r_{7}\,\cos({\theta_{7}
1628
})\,r_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}} \end{eqnarray*}
1629
\begin{eqnarray*} && m_{2}\,g\,r_{2}\,\cos({\theta_{2}}) + 2\,r_{2}\,
1630
\cos({\theta_{2}})\,m_{6}\,g + 2\,r_{2}\,\cos({\theta_{2}})\,m_{3}\,g
1631
+ 2\,r_{2}\,\cos({\theta_{2}})\,m_{4}\,g + 2\,r_{2}\,\cos({\theta_{2}
1632
})\,m_{5}\,g \\ &&\quad\mbox{} + 2\,r_{2}\,\cos({\theta_{2}})\,m_{9}\,
1633
g + 2\,r_{2}\,\cos({\theta_{2}})\,m_{8}\,g + 2\,r_{2}\,\cos({\theta_{2
1634
}})\,m_{7}\,g + 2\,r_{2}\,\cos({\theta_{2}})\,m_{10}\,g + 4\,{r_{2}}^2
1635
\,m_{10}\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} + 4\,{r_{2}}^2\,m_{5}\,{
1636
\dot{\eta}_{2}} + 4\,{r_{2}}^2\,m_{4}\,{\dot{\eta}_{2}} + 4\,{r_{2}}^2
1637
\,m_{3}\,{\dot{\eta}_{2}} + 4\,{r_{2}}^2\,m_{7}\,{\dot{\eta}_{2}} + 4
1638
\,{r_{2}}^2\,m_{6}\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} + 4\,{r_{2}}^2
1639
\,m_{8}\,{\dot{\eta}_{2}} + 4\,{r_{2}}^2\,m_{9}\,{\dot{\eta}_{2}} + J
1640
_{2}\,{\dot{\eta}_{2}} + 4\,r_{2}\,\cos({\theta_{2}})\,m_{4}\,r_{1}\,
1641
\cos({\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} - 4\,r_{2}\,
1642
\cos({\theta_{2}})\,m_{3}\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2
1643
+ 4\,r_{2}\,\cos({\theta_{2}})\,m_{3}\,r_{1}\,\cos({\theta_{1}})\,{
1644
\dot{\eta}_{1}} \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{4
1645
}\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} + 4\,r_{2}\,\cos({
1646
\theta_{2}})\,m_{10}\,r_{7}\,\cos({\theta_{7}})\,{\dot{\eta}_{7}}
1647
\\ &&\quad\mbox{} - 4\,r_{2}\,\cos({\theta_{2}})\,m_{10}\,r_{3}\,\sin
1648
({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{2}\,\cos({\theta_{2}})\,m_{10}
1649
\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} - 4\,r
1650
_{2}\,\cos({\theta_{2}})\,m_{10}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4
1651
}}}^2 - 4\,r_{2}\,\cos({\theta_{2}})\,m_{10}\,r_{1}\,\sin({\theta_{1}}
1652
)\,{{\eta_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m
1653
_{10}\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} - 4\,r_{2}\,\cos({
1654
\theta_{2}})\,m_{10}\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2
1655
\\ &&\quad\mbox{} + 4\,r_{2}\,\cos({\theta_{2}})\,m_{10}\,r_{5}\,\cos
1656
({\theta_{5}})\,{\dot{\eta}_{5}} - 4\,r_{2}\,\cos({\theta_{2}})\,m_{10
1657
}\,r_{8}\,\sin({\theta_{8}})\,{{\eta_{8}}}^2 \\ &&\quad\mbox{} + 4\,r
1658
_{2}\,\cos({\theta_{2}})\,m_{10}\,r_{4}\,\cos({\theta_{4}})\,{
1659
\dot{\eta}_{4}} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{10}\,r_{5}\,\cos({
1660
\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({
1661
\theta_{2}})\,m_{10}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r
1662
_{2}\,\sin({\theta_{2}})\,m_{10}\,r_{4}\,\sin({\theta_{4}})\,{
1663
\dot{\eta}_{4}} \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{
1664
10}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2 - 4\,r_{2}\,\cos({
1665
\theta_{2}})\,m_{10}\,r_{6}\,\sin({\theta_{6}})\,{{\eta_{6}}}^2
1666
\\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{10}\,r_{3}\,\sin
1667
({\theta_{3}})\,{\dot{\eta}_{3}} + 4\,r_{2}\,\cos({\theta_{2}})\,m_{10
1668
}\,r_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} + 4\,
1669
r_{2}\,\cos({\theta_{2}})\,m_{10}\,r_{8}\,\cos({\theta_{8}})\,{
1670
\dot{\eta}_{8}} - 4\,r_{2}\,\cos({\theta_{2}})\,m_{10}\,r_{7}\,\sin({
1671
\theta_{7}})\,{{\eta_{7}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}\,\cos({
1672
\theta_{2}})\,m_{10}\,r_{1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1}} + 4
1673
\,r_{2}\,\sin({\theta_{2}})\,m_{3}\,r_{1}\,\cos({\theta_{1}})\,{{\eta
1674
_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}\,\cos({\theta_{2}})\,m_{4}\,r_{3
1675
}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}} + 2\,m_{2}\,r_{2}\,\sin({
1676
\theta_{2}})\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2
1677
\\ &&\quad\mbox{} - 4\,r_{2}\,\cos({\theta_{2}})\,m_{4}\,r_{1}\,\sin(
1678
{\theta_{1}})\,{{\eta_{1}}}^2 + 4\,r_{2}\,\sin({\theta_{2}})\,m_{10}\,
1679
r_{9}\,\cos({\theta_{9}})\,{{\eta_{9}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}
1680
\,\sin({\theta_{2}})\,m_{10}\,r_{9}\,\sin({\theta_{9}})\,{\dot{\eta}_{
1681
9}} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{10}\,r_{8}\,\cos({\theta_{8}})
1682
\,{{\eta_{8}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{
1683
10}\,r_{8}\,\sin({\theta_{8}})\,{\dot{\eta}_{8}} + 4\,r_{2}\,\sin({
1684
\theta_{2}})\,m_{10}\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}}
1685
\\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{10}\,r_{7}\,\cos
1686
({\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{2}\,\sin({\theta_{2}})\,m_{10}
1687
\,r_{7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}} \\ &&\quad\mbox{} + 4\,r
1688
_{2}\,\sin({\theta_{2}})\,m_{10}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6
1689
}}}^2 + 4\,r_{2}\,\sin({\theta_{2}})\,m_{10}\,r_{6}\,\sin({\theta_{6}}
1690
)\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,
1691
m_{10}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{2}\,\sin({
1692
\theta_{2}})\,m_{4}\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}}
1693
\\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{4}\,r_{1}\,\cos(
1694
{\theta_{1}})\,{{\eta_{1}}}^2 + 2\,r_{2}\,\sin({\theta_{2}})\,m_{8}\,r
1695
_{8}\,\sin({\theta_{8}})\,{\dot{\eta}_{8}} \\ &&\quad\mbox{} + 2\,r_{2
1696
}\,\cos({\theta_{2}})\,m_{8}\,r_{8}\,\cos({\theta_{8}})\,{\dot{\eta}_{
1697
8}} + 2\,r_{2}\,\cos({\theta_{2}})\,m_{9}\,r_{9}\,\cos({\theta_{9}})\,
1698
{\dot{\eta}_{9}} \\ &&\quad\mbox{} + 2\,r_{2}\,\sin({\theta_{2}})\,m_{
1699
9}\,r_{9}\,\sin({\theta_{9}})\,{\dot{\eta}_{9}} + 2\,r_{2}\,\sin({
1700
\theta_{2}})\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,{\dot{\eta}_{10}}
1701
\\ &&\quad\mbox{} + 2\,r_{2}\,\cos({\theta_{2}})\,m_{10}\,r_{10}\,
1702
\cos({\theta_{10}})\,{\dot{\eta}_{10}} + 4\,r_{2}\,\sin({\theta_{2}})
1703
\,m_{4}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{}
1704
- 4\,r_{2}\,\cos({\theta_{2}})\,m_{4}\,r_{3}\,\sin({\theta_{3}})\,{{
1705
\eta_{3}}}^2 - 4\,r_{2}\,\cos({\theta_{2}})\,m_{5}\,r_{4}\,\sin({
1706
\theta_{4}})\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({
1707
\theta_{2}})\,m_{5}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r
1708
_{2}\,\sin({\theta_{2}})\,m_{5}\,r_{4}\,\sin({\theta_{4}})\,{
1709
\dot{\eta}_{4}} \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{5
1710
}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{2}\,\sin({\theta
1711
_{2}})\,m_{5}\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}}
1712
\\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{6}\,r_{5}\,\cos(
1713
{\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{2}\,\cos({\theta_{2}})\,m_{7}\,r
1714
_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} + 4\,r_{2
1715
}\,\sin({\theta_{2}})\,m_{7}\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{
1716
1}} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{7}\,r_{4}\,\cos({\theta_{4}})\,
1717
{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{7}
1718
\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}} + 4\,r_{2}\,\sin({\theta
1719
_{2}})\,m_{7}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2
1720
\\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{7}\,r_{3}\,\cos(
1721
{\theta_{3}})\,{{\eta_{3}}}^2 - 4\,r_{2}\,\cos({\theta_{2}})\,m_{7}\,r
1722
_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}
1723
\,\sin({\theta_{2}})\,m_{8}\,r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}_{6
1724
}} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{8}\,r_{7}\,\cos({\theta_{7}})\,{
1725
{\eta_{7}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}\,\cos({\theta_{2}})\,m_{7}
1726
\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}} - 4\,r_{2}\,\cos({\theta
1727
_{2}})\,m_{7}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^2 + m_{2}\,{r_{
1728
2}}^2\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} + 4\,r_{2}\,\cos({\theta_{2}
1729
})\,m_{6}\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}} + 4\,r_{2}\,
1730
\sin({\theta_{2}})\,m_{6}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2
1731
\\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{6}\,r_{3}\,\sin(
1732
{\theta_{3}})\,{\dot{\eta}_{3}} - 4\,r_{2}\,\cos({\theta_{2}})\,m_{6}
1733
\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 4\,r_{
1734
2}\,\cos({\theta_{2}})\,m_{6}\,r_{5}\,\cos({\theta_{5}})\,{\dot{\eta}
1735
_{5}} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{6}\,r_{1}\,\cos({\theta_{1}})
1736
\,{{\eta_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}\,\cos({\theta_{2}})\,m_{
1737
6}\,r_{1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1}} - 4\,r_{2}\,\cos({
1738
\theta_{2}})\,m_{6}\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2
1739
\\ &&\quad\mbox{} + 4\,r_{2}\,\cos({\theta_{2}})\,m_{6}\,r_{3}\,\cos(
1740
{\theta_{3}})\,{\dot{\eta}_{3}} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{6}
1741
\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} - 4\,r
1742
_{2}\,\cos({\theta_{2}})\,m_{6}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}
1743
}}^2 + 4\,r_{2}\,\sin({\theta_{2}})\,m_{7}\,r_{3}\,\sin({\theta_{3}})
1744
\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m
1745
_{7}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{2}\,\sin({
1746
\theta_{2}})\,m_{7}\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}}
1747
\\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{7}\,r_{6}\,\cos(
1748
{\theta_{6}})\,{{\eta_{6}}}^2 + 4\,r_{2}\,\sin({\theta_{2}})\,m_{7}\,r
1749
_{6}\,\sin({\theta_{6}})\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} - 4\,r_{2
1750
}\,\cos({\theta_{2}})\,m_{6}\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^
1751
2 + 4\,r_{2}\,\sin({\theta_{2}})\,m_{6}\,r_{5}\,\sin({\theta_{5}})\,{
1752
\dot{\eta}_{5}} \\ &&\quad\mbox{} - 4\,r_{2}\,\cos({\theta_{2}})\,m_{5
1753
}\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2 + 4\,r_{2}\,\cos({\theta
1754
_{2}})\,m_{5}\,r_{1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1}}
1755
\\ &&\quad\mbox{} - 4\,r_{2}\,\cos({\theta_{2}})\,m_{5}\,r_{3}\,\sin(
1756
{\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{2}\,\cos({\theta_{2}})\,m_{5}\,r
1757
_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,r_{2
1758
}\,\sin({\theta_{2}})\,m_{6}\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{
1759
1}} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{6}\,r_{4}\,\cos({\theta_{4}})\,
1760
{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}\,\cos({\theta_{2}})\,m_{5}
1761
\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}} + 4\,r_{2}\,\sin({\theta
1762
_{2}})\,m_{5}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2
1763
\\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{5}\,r_{1}\,\sin(
1764
{\theta_{1}})\,{\dot{\eta}_{1}} + 2\,m_{2}\,r_{2}\,\sin({\theta_{2}})
1765
\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} + 4\,r
1766
_{2}\,\sin({\theta_{2}})\,m_{3}\,r_{1}\,\sin({\theta_{1}})\,{
1767
\dot{\eta}_{1}} - 2\,r_{2}\,\cos({\theta_{2}})\,m_{3}\,r_{3}\,\sin({
1768
\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} + 2\,r_{2}\,\sin({
1769
\theta_{2}})\,m_{3}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2 + 2\,r
1770
_{2}\,\sin({\theta_{2}})\,m_{4}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}
1771
}}^2 \\ &&\quad\mbox{} - 2\,r_{2}\,\cos({\theta_{2}})\,m_{4}\,r_{4}\,
1772
\sin({\theta_{4}})\,{{\eta_{4}}}^2 + 2\,r_{2}\,\sin({\theta_{2}})\,m_{
1773
5}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} - 2\,r
1774
_{2}\,\cos({\theta_{2}})\,m_{5}\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}
1775
}}^2 - 2\,r_{2}\,\cos({\theta_{2}})\,m_{6}\,r_{6}\,\sin({\theta_{6}})
1776
\,{{\eta_{6}}}^2 \\ &&\quad\mbox{} + 2\,r_{2}\,\sin({\theta_{2}})\,m_{
1777
6}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2 - 2\,r_{2}\,\cos({\theta
1778
_{2}})\,m_{7}\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7}}}^2
1779
\\ &&\quad\mbox{} + 2\,r_{2}\,\sin({\theta_{2}})\,m_{7}\,r_{7}\,\cos(
1780
{\theta_{7}})\,{{\eta_{7}}}^2 + 2\,r_{2}\,\sin({\theta_{2}})\,m_{8}\,r
1781
_{8}\,\cos({\theta_{8}})\,{{\eta_{8}}}^2 \\ &&\quad\mbox{} - 2\,r_{2}
1782
\,\cos({\theta_{2}})\,m_{8}\,r_{8}\,\sin({\theta_{8}})\,{{\eta_{8}}}^2
1783
- 2\,r_{2}\,\cos({\theta_{2}})\,m_{9}\,r_{9}\,\sin({\theta_{9}})\,{{
1784
\eta_{9}}}^2 \\ &&\quad\mbox{} + 2\,r_{2}\,\sin({\theta_{2}})\,m_{9}\,
1785
r_{9}\,\cos({\theta_{9}})\,{{\eta_{9}}}^2 + 2\,r_{2}\,\sin({\theta_{2}
1786
})\,m_{10}\,r_{10}\,\cos({\theta_{10}})\,{{\eta_{10}}}^2
1787
\\ &&\quad\mbox{} - 2\,r_{2}\,\cos({\theta_{2}})\,m_{10}\,r_{10}\,
1788
\sin({\theta_{10}})\,{{\eta_{10}}}^2 - 4\,r_{2}\,\cos({\theta_{2}})\,m
1789
_{10}\,r_{9}\,\sin({\theta_{9}})\,{{\eta_{9}}}^2 \\ &&\quad\mbox{} + 4
1790
\,r_{2}\,\cos({\theta_{2}})\,m_{10}\,r_{9}\,\cos({\theta_{9}})\,{
1791
\dot{\eta}_{9}} + 4\,r_{2}\,\cos({\theta_{2}})\,m_{8}\,r_{5}\,\cos({
1792
\theta_{5}})\,{\dot{\eta}_{5}} \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({
1793
\theta_{2}})\,m_{8}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2 + 2\,m
1794
_{2}\,r_{2}\,\cos({\theta_{2}})\,r_{1}\,\cos({\theta_{1}})\,{
1795
\dot{\eta}_{1}} \\ &&\quad\mbox{} + 4\,r_{2}\,\cos({\theta_{2}})\,m_{8
1796
}\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}} - 2\,m_{2}\,r_{2}\,\cos
1797
({\theta_{2}})\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2
1798
\\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{9}\,r_{4}\,\cos(
1799
{\theta_{4}})\,{{\eta_{4}}}^2 - 4\,r_{2}\,\cos({\theta_{2}})\,m_{9}\,r
1800
_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}
1801
\,\cos({\theta_{2}})\,m_{9}\,r_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6
1802
}} + 4\,r_{2}\,\cos({\theta_{2}})\,m_{9}\,r_{1}\,\cos({\theta_{1}})\,{
1803
\dot{\eta}_{1}} \\ &&\quad\mbox{} - 4\,r_{2}\,\cos({\theta_{2}})\,m_{9
1804
}\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{2}\,\cos({\theta
1805
_{2}})\,m_{9}\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}}
1806
\\ &&\quad\mbox{} - 4\,r_{2}\,\cos({\theta_{2}})\,m_{8}\,r_{3}\,\sin(
1807
{\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{2}\,\sin({\theta_{2}})\,m_{9}\,r
1808
_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}
1809
\,\sin({\theta_{2}})\,m_{9}\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5
1810
}} - 4\,r_{2}\,\cos({\theta_{2}})\,m_{8}\,r_{4}\,\sin({\theta_{4}})\,{
1811
{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}\,\cos({\theta_{2}})\,m_{8}
1812
\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}} - 4\,r_{2}\,\cos({\theta
1813
_{2}})\,m_{8}\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2
1814
\\ &&\quad\mbox{} - 4\,r_{2}\,\cos({\theta_{2}})\,m_{8}\,r_{1}\,\sin(
1815
{\theta_{1}})\,{{\eta_{1}}}^2 - 4\,r_{2}\,\cos({\theta_{2}})\,m_{8}\,r
1816
_{7}\,\sin({\theta_{7}})\,{{\eta_{7}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}
1817
\,\cos({\theta_{2}})\,m_{8}\,r_{7}\,\cos({\theta_{7}})\,{\dot{\eta}_{7
1818
}} - 4\,r_{2}\,\cos({\theta_{2}})\,m_{8}\,r_{6}\,\sin({\theta_{6}})\,{
1819
{\eta_{6}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{8}
1820
\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}} + 4\,r_{2}\,\cos({\theta
1821
_{2}})\,m_{8}\,r_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}}
1822
\\ &&\quad\mbox{} + 4\,r_{2}\,\cos({\theta_{2}})\,m_{8}\,r_{1}\,\cos(
1823
{\theta_{1}})\,{\dot{\eta}_{1}} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{9}
1824
\,r_{8}\,\cos({\theta_{8}})\,{{\eta_{8}}}^2 \\ &&\quad\mbox{} + 4\,r_{
1825
2}\,\sin({\theta_{2}})\,m_{9}\,r_{8}\,\sin({\theta_{8}})\,{\dot{\eta}
1826
_{8}} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{9}\,r_{7}\,\cos({\theta_{7}})
1827
\,{{\eta_{7}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{
1828
9}\,r_{7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}} + 4\,r_{2}\,\sin({
1829
\theta_{2}})\,m_{9}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2
1830
\\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{9}\,r_{6}\,\sin(
1831
{\theta_{6}})\,{\dot{\eta}_{6}} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{8}
1832
\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} + 4\,r
1833
_{2}\,\sin({\theta_{2}})\,m_{8}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}
1834
}}^2 + 4\,r_{2}\,\sin({\theta_{2}})\,m_{8}\,r_{4}\,\sin({\theta_{4}})
1835
\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m
1836
_{8}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{2}\,\sin({
1837
\theta_{2}})\,m_{8}\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}}
1838
\\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{8}\,r_{5}\,\cos(
1839
{\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{2}\,\cos({\theta_{2}})\,m_{7}\,r
1840
_{1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} - 4\,r_{2
1841
}\,\cos({\theta_{2}})\,m_{7}\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^
1842
2 + 4\,r_{2}\,\sin({\theta_{2}})\,m_{8}\,r_{7}\,\sin({\theta_{7}})\,{
1843
\dot{\eta}_{7}} \\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{8
1844
}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2 + 4\,r_{2}\,\cos({\theta
1845
_{2}})\,m_{7}\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}}
1846
\\ &&\quad\mbox{} - 4\,r_{2}\,\cos({\theta_{2}})\,m_{7}\,r_{5}\,\sin(
1847
{\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{2}\,\cos({\theta_{2}})\,m_{7}\,r
1848
_{5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5}} \\ &&\quad\mbox{} - 4\,r_{2
1849
}\,\cos({\theta_{2}})\,m_{7}\,r_{6}\,\sin({\theta_{6}})\,{{\eta_{6}}}^
1850
2 + 4\,r_{2}\,\cos({\theta_{2}})\,m_{9}\,r_{7}\,\cos({\theta_{7}})\,{
1851
\dot{\eta}_{7}} \\ &&\quad\mbox{} - 4\,r_{2}\,\cos({\theta_{2}})\,m_{9
1852
}\,r_{6}\,\sin({\theta_{6}})\,{{\eta_{6}}}^2 - 4\,r_{2}\,\cos({\theta
1853
_{2}})\,m_{9}\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7}}}^2
1854
\\ &&\quad\mbox{} - 4\,r_{2}\,\cos({\theta_{2}})\,m_{9}\,r_{1}\,\sin(
1855
{\theta_{1}})\,{{\eta_{1}}}^2 - 4\,r_{2}\,\cos({\theta_{2}})\,m_{9}\,r
1856
_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}
1857
\,\cos({\theta_{2}})\,m_{9}\,r_{5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5
1858
}} - 4\,r_{2}\,\cos({\theta_{2}})\,m_{9}\,r_{8}\,\sin({\theta_{8}})\,{
1859
{\eta_{8}}}^2 \\ &&\quad\mbox{} + 4\,r_{2}\,\cos({\theta_{2}})\,m_{9}
1860
\,r_{8}\,\cos({\theta_{8}})\,{\dot{\eta}_{8}} + 4\,r_{2}\,\sin({\theta
1861
_{2}})\,m_{9}\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}}
1862
\\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{9}\,r_{3}\,\cos(
1863
{\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{2}\,\sin({\theta_{2}})\,m_{9}\,r
1864
_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,r_{2
1865
}\,\cos({\theta_{2}})\,m_{9}\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{
1866
4}} + 2\,r_{2}\,\cos({\theta_{2}})\,m_{3}\,r_{3}\,\cos({\theta_{3}})\,
1867
{\dot{\eta}_{3}} \\ &&\quad\mbox{} + 2\,r_{2}\,\sin({\theta_{2}})\,m_{
1868
3}\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}} + 2\,r_{2}\,\sin({
1869
\theta_{2}})\,m_{4}\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}}
1870
\\ &&\quad\mbox{} + 2\,r_{2}\,\cos({\theta_{2}})\,m_{4}\,r_{4}\,\cos(
1871
{\theta_{4}})\,{\dot{\eta}_{4}} + 2\,r_{2}\,\sin({\theta_{2}})\,m_{5}
1872
\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}} \\ &&\quad\mbox{} + 2\,r
1873
_{2}\,\cos({\theta_{2}})\,m_{5}\,r_{5}\,\cos({\theta_{5}})\,{
1874
\dot{\eta}_{5}} + 2\,r_{2}\,\cos({\theta_{2}})\,m_{6}\,r_{6}\,\cos({
1875
\theta_{6}})\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} + 2\,r_{2}\,\sin({
1876
\theta_{2}})\,m_{6}\,r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}_{6}} + 2\,
1877
r_{2}\,\cos({\theta_{2}})\,m_{7}\,r_{7}\,\cos({\theta_{7}})\,{
1878
\dot{\eta}_{7}} \\ &&\quad\mbox{} + 2\,r_{2}\,\sin({\theta_{2}})\,m_{7
1879
}\,r_{7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}} + 4\,r_{2}\,\sin({
1880
\theta_{2}})\,m_{9}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2
1881
\\ &&\quad\mbox{} + 4\,r_{2}\,\sin({\theta_{2}})\,m_{9}\,r_{1}\,\sin(
1882
{\theta_{1}})\,{\dot{\eta}_{1}} \end{eqnarray*}
1883
\begin{eqnarray*} && 4\,{r_{1}}^2\,m_{3}\,{\dot{\eta}_{1}} + 4\,{r_{1}
1884
}^2\,m_{8}\,{\dot{\eta}_{1}} + m_{1}\,g\,r_{1}\,\cos({\theta_{1}}) + 4
1885
\,{r_{1}}^2\,m_{5}\,{\dot{\eta}_{1}} + 4\,{r_{1}}^2\,m_{10}\,{
1886
\dot{\eta}_{1}} \\ &&\quad\mbox{} - 2\,r_{1}\,\cos({\theta_{1}})\,m_{9
1887
}\,r_{9}\,\sin({\theta_{9}})\,{{\eta_{9}}}^2 + 2\,r_{1}\,\sin({\theta
1888
_{1}})\,m_{9}\,r_{9}\,\cos({\theta_{9}})\,{{\eta_{9}}}^2 + 4\,{r_{1}}^
1889
2\,m_{4}\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} + 4\,{r_{1}}^2\,m_{7}\,{
1890
\dot{\eta}_{1}} + 4\,{r_{1}}^2\,m_{6}\,{\dot{\eta}_{1}} + 4\,{r_{1}}^2
1891
\,m_{9}\,{\dot{\eta}_{1}} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{10}\,r_{4
1892
}\,\cos({\theta_{4}})\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{1}\,
1893
\sin({\theta_{1}})\,m_{3}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2
1894
+ 4\,r_{1}\,\sin({\theta_{1}})\,m_{3}\,r_{2}\,\sin({\theta_{2}})\,{
1895
\dot{\eta}_{2}} \\ &&\quad\mbox{} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{3
1896
}\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{1}\,\cos({\theta
1897
_{1}})\,m_{3}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}}
1898
\\ &&\quad\mbox{} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{9}\,r_{3}\,\sin(
1899
{\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{1}\,\cos({\theta_{1}})\,m_{9}\,r
1900
_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} - 4\,r_{1
1901
}\,\cos({\theta_{1}})\,m_{9}\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^
1902
2 + 4\,r_{1}\,\cos({\theta_{1}})\,m_{9}\,r_{2}\,\cos({\theta_{2}})\,{
1903
\dot{\eta}_{2}} \\ &&\quad\mbox{} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{9
1904
}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r_{1}\,\cos({\theta
1905
_{1}})\,m_{9}\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}}
1906
\\ &&\quad\mbox{} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{9}\,r_{5}\,\sin(
1907
{\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{1}\,\cos({\theta_{1}})\,m_{9}\,r
1908
_{5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5}} \\ &&\quad\mbox{} - 4\,r_{1
1909
}\,\cos({\theta_{1}})\,m_{9}\,r_{8}\,\sin({\theta_{8}})\,{{\eta_{8}}}^
1910
2 + 4\,r_{1}\,\cos({\theta_{1}})\,m_{9}\,r_{8}\,\cos({\theta_{8}})\,{
1911
\dot{\eta}_{8}} \\ &&\quad\mbox{} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{9
1912
}\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{1}\,\sin({\theta
1913
_{1}})\,m_{9}\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}}
1914
\\ &&\quad\mbox{} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{9}\,r_{2}\,\cos(
1915
{\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{1}\,\sin({\theta_{1}})\,m_{9}\,r
1916
_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} + 4\,r_{1
1917
}\,\sin({\theta_{1}})\,m_{9}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^
1918
2 + 4\,r_{1}\,\sin({\theta_{1}})\,m_{9}\,r_{5}\,\sin({\theta_{5}})\,{
1919
\dot{\eta}_{5}} \\ &&\quad\mbox{} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{9
1920
}\,r_{8}\,\cos({\theta_{8}})\,{{\eta_{8}}}^2 + 4\,r_{1}\,\sin({\theta
1921
_{1}})\,m_{9}\,r_{8}\,\sin({\theta_{8}})\,{\dot{\eta}_{8}}
1922
\\ &&\quad\mbox{} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{9}\,r_{7}\,\cos(
1923
{\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{1}\,\sin({\theta_{1}})\,m_{9}\,r
1924
_{7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}} \\ &&\quad\mbox{} + 4\,r_{1
1925
}\,\sin({\theta_{1}})\,m_{9}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^
1926
2 + 4\,r_{1}\,\sin({\theta_{1}})\,m_{9}\,r_{6}\,\sin({\theta_{6}})\,{
1927
\dot{\eta}_{6}} \\ &&\quad\mbox{} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{8
1928
}\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{1}\,\cos({\theta
1929
_{1}})\,m_{8}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}}
1930
\\ &&\quad\mbox{} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{8}\,r_{4}\,\sin(
1931
{\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r_{1}\,\cos({\theta_{1}})\,m_{8}\,r
1932
_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} - 4\,r_{1
1933
}\,\cos({\theta_{1}})\,m_{8}\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^
1934
2 + 4\,r_{1}\,\cos({\theta_{1}})\,m_{8}\,r_{5}\,\cos({\theta_{5}})\,{
1935
\dot{\eta}_{5}} \\ &&\quad\mbox{} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{8
1936
}\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{1}\,\cos({\theta
1937
_{1}})\,m_{8}\,r_{7}\,\cos({\theta_{7}})\,{\dot{\eta}_{7}}
1938
\\ &&\quad\mbox{} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{8}\,r_{6}\,\sin(
1939
{\theta_{6}})\,{{\eta_{6}}}^2 + 4\,r_{1}\,\cos({\theta_{1}})\,m_{8}\,r
1940
_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} + 4\,r_{1
1941
}\,\sin({\theta_{1}})\,m_{6}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^
1942
2 + 4\,r_{1}\,\sin({\theta_{1}})\,m_{6}\,r_{4}\,\sin({\theta_{4}})\,{
1943
\dot{\eta}_{4}} \\ &&\quad\mbox{} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{6
1944
}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{1}\,\sin({\theta
1945
_{1}})\,m_{6}\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}}
1946
\\ &&\quad\mbox{} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{6}\,r_{2}\,\cos(
1947
{\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{1}\,\sin({\theta_{1}})\,m_{6}\,r
1948
_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} + 4\,r_{1
1949
}\,\sin({\theta_{1}})\,m_{6}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^
1950
2 + 4\,r_{1}\,\sin({\theta_{1}})\,m_{6}\,r_{5}\,\sin({\theta_{5}})\,{
1951
\dot{\eta}_{5}} \\ &&\quad\mbox{} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{9
1952
}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r_{1}\,\sin({\theta
1953
_{1}})\,m_{9}\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}}
1954
\\ &&\quad\mbox{} + 4\,r_{1}\,\cos({\theta_{1}})\,m_{8}\,r_{3}\,\cos(
1955
{\theta_{3}})\,{\dot{\eta}_{3}} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{9}
1956
\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} + 4\,r_{
1957
1}\,\sin({\theta_{1}})\,m_{7}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}
1958
^2 + 4\,r_{1}\,\sin({\theta_{1}})\,m_{7}\,r_{5}\,\sin({\theta_{5}})\,{
1959
\dot{\eta}_{5}} \\ &&\quad\mbox{} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{7
1960
}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2 + 4\,r_{1}\,\sin({\theta
1961
_{1}})\,m_{7}\,r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}_{6}}
1962
\\ &&\quad\mbox{} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{4}\,r_{3}\,\sin(
1963
{\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{1}\,\cos({\theta_{1}})\,m_{4}\,r
1964
_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} - 4\,r_{1
1965
}\,\cos({\theta_{1}})\,m_{4}\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^
1966
2 + 4\,r_{1}\,\cos({\theta_{1}})\,m_{4}\,r_{2}\,\cos({\theta_{2}})\,{
1967
\dot{\eta}_{2}} \\ &&\quad\mbox{} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{6
1968
}\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{1}\,\cos({\theta
1969
_{1}})\,m_{6}\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}}
1970
\\ &&\quad\mbox{} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{6}\,r_{2}\,\sin(
1971
{\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{1}\,\cos({\theta_{1}})\,m_{6}\,r
1972
_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} - 4\,r_{1
1973
}\,\cos({\theta_{1}})\,m_{6}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^
1974
2 + 4\,r_{1}\,\cos({\theta_{1}})\,m_{6}\,r_{4}\,\cos({\theta_{4}})\,{
1975
\dot{\eta}_{4}} \\ &&\quad\mbox{} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{6
1976
}\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{1}\,\cos({\theta
1977
_{1}})\,m_{6}\,r_{5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5}}
1978
\\ &&\quad\mbox{} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{7}\,r_{4}\,\cos(
1979
{\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r_{1}\,\sin({\theta_{1}})\,m_{8}\,r
1980
_{7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}} \\ &&\quad\mbox{} + 4\,r_{1
1981
}\,\sin({\theta_{1}})\,m_{8}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^
1982
2 + 4\,r_{1}\,\sin({\theta_{1}})\,m_{8}\,r_{6}\,\sin({\theta_{6}})\,{
1983
\dot{\eta}_{6}} \\ &&\quad\mbox{} + 4\,r_{1}\,\cos({\theta_{1}})\,m_{5
1984
}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}} - 4\,r_{1}\,\cos({
1985
\theta_{1}})\,m_{5}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^2
1986
\\ &&\quad\mbox{} + 4\,r_{1}\,\cos({\theta_{1}})\,m_{5}\,r_{4}\,\cos(
1987
{\theta_{4}})\,{\dot{\eta}_{4}} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{7}
1988
\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} + 4\,r_{
1989
1}\,\cos({\theta_{1}})\,m_{7}\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}
1990
_{3}} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{7}\,r_{2}\,\sin({\theta_{2}})
1991
\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{1}\,\cos({\theta_{1}})\,m_{
1992
7}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}} - 4\,r_{1}\,\cos({
1993
\theta_{1}})\,m_{10}\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2
1994
\\ &&\quad\mbox{} + 4\,r_{1}\,\cos({\theta_{1}})\,m_{10}\,r_{5}\,\cos
1995
({\theta_{5}})\,{\dot{\eta}_{5}} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{10
1996
}\,r_{8}\,\sin({\theta_{8}})\,{{\eta_{8}}}^2 \\ &&\quad\mbox{} + 4\,r
1997
_{1}\,\cos({\theta_{1}})\,m_{10}\,r_{8}\,\cos({\theta_{8}})\,{
1998
\dot{\eta}_{8}} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{10}\,r_{9}\,\sin({
1999
\theta_{9}})\,{{\eta_{9}}}^2 \\ &&\quad\mbox{} + 4\,r_{1}\,\cos({
2000
\theta_{1}})\,m_{10}\,r_{9}\,\cos({\theta_{9}})\,{\dot{\eta}_{9}} - 4
2001
\,r_{1}\,\cos({\theta_{1}})\,m_{10}\,r_{7}\,\sin({\theta_{7}})\,{{\eta
2002
_{7}}}^2 \\ &&\quad\mbox{} + 4\,r_{1}\,\cos({\theta_{1}})\,m_{10}\,r_{
2003
7}\,\cos({\theta_{7}})\,{\dot{\eta}_{7}} - 4\,r_{1}\,\cos({\theta_{1}}
2004
)\,m_{10}\,r_{6}\,\sin({\theta_{6}})\,{{\eta_{6}}}^2 \\ &&\quad\mbox{}
2005
+ 4\,r_{1}\,\cos({\theta_{1}})\,m_{10}\,r_{6}\,\cos({\theta_{6}})\,{
2006
\dot{\eta}_{6}} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{10}\,r_{3}\,\sin({
2007
\theta_{3}})\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,r_{1}\,\sin({
2008
\theta_{1}})\,m_{10}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r
2009
_{1}\,\sin({\theta_{1}})\,m_{10}\,r_{2}\,\sin({\theta_{2}})\,{
2010
\dot{\eta}_{2}} \\ &&\quad\mbox{} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{
2011
10}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^2 + 4\,r_{1}\,\sin({
2012
\theta_{1}})\,m_{10}\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}}
2013
\\ &&\quad\mbox{} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{10}\,r_{9}\,\cos
2014
({\theta_{9}})\,{{\eta_{9}}}^2 + 4\,r_{1}\,\sin({\theta_{1}})\,m_{10}
2015
\,r_{9}\,\sin({\theta_{9}})\,{\dot{\eta}_{9}} \\ &&\quad\mbox{} + 4\,r
2016
_{1}\,\sin({\theta_{1}})\,m_{10}\,r_{8}\,\cos({\theta_{8}})\,{{\eta_{8
2017
}}}^2 + 4\,r_{1}\,\sin({\theta_{1}})\,m_{10}\,r_{8}\,\sin({\theta_{8}}
2018
)\,{\dot{\eta}_{8}} \\ &&\quad\mbox{} - 4\,r_{1}\,\cos({\theta_{1}})\,
2019
m_{9}\,r_{6}\,\sin({\theta_{6}})\,{{\eta_{6}}}^2 + 4\,r_{1}\,\cos({
2020
\theta_{1}})\,m_{9}\,r_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}}
2021
\\ &&\quad\mbox{} + 4\,r_{1}\,\cos({\theta_{1}})\,m_{7}\,r_{5}\,\cos(
2022
{\theta_{5}})\,{\dot{\eta}_{5}} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{7}
2023
\,r_{6}\,\sin({\theta_{6}})\,{{\eta_{6}}}^2 \\ &&\quad\mbox{} + 4\,r_{
2024
1}\,\cos({\theta_{1}})\,m_{7}\,r_{6}\,\cos({\theta_{6}})\,{\dot{\eta}
2025
_{6}} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{8}\,r_{4}\,\cos({\theta_{4}})
2026
\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{
2027
8}\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}} + 4\,r_{1}\,\sin({
2028
\theta_{1}})\,m_{8}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2
2029
\\ &&\quad\mbox{} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{8}\,r_{3}\,\sin(
2030
{\theta_{3}})\,{\dot{\eta}_{3}} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{8}
2031
\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{
2032
1}\,\sin({\theta_{1}})\,m_{8}\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}
2033
_{2}} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{8}\,r_{5}\,\cos({\theta_{5}})
2034
\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{
2035
8}\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}} + 4\,r_{1}\,\sin({
2036
\theta_{1}})\,m_{10}\,r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^2
2037
\\ &&\quad\mbox{} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{10}\,r_{7}\,\sin
2038
({\theta_{7}})\,{\dot{\eta}_{7}} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{10
2039
}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2 \\ &&\quad\mbox{} + 4\,r
2040
_{1}\,\sin({\theta_{1}})\,m_{10}\,r_{6}\,\sin({\theta_{6}})\,{
2041
\dot{\eta}_{6}} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{10}\,r_{3}\,\sin({
2042
\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} + 4\,r_{1}\,\cos({
2043
\theta_{1}})\,m_{10}\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}} - 4
2044
\,r_{1}\,\cos({\theta_{1}})\,m_{10}\,r_{2}\,\sin({\theta_{2}})\,{{\eta
2045
_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{1}\,\cos({\theta_{1}})\,m_{9}\,r_{7
2046
}\,\cos({\theta_{7}})\,{\dot{\eta}_{7}} + 4\,r_{1}\,\sin({\theta_{1}})
2047
\,m_{8}\,r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^2 \\ &&\quad\mbox{}
2048
- 4\,r_{1}\,\cos({\theta_{1}})\,m_{7}\,r_{4}\,\sin({\theta_{4}})\,{{
2049
\eta_{4}}}^2 + 4\,r_{1}\,\cos({\theta_{1}})\,m_{7}\,r_{4}\,\cos({
2050
\theta_{4}})\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} + 4\,r_{1}\,\sin({
2051
\theta_{1}})\,m_{5}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^2 + 4\,r
2052
_{1}\,\sin({\theta_{1}})\,m_{5}\,r_{4}\,\sin({\theta_{4}})\,{
2053
\dot{\eta}_{4}} \\ &&\quad\mbox{} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{5
2054
}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{1}\,\sin({\theta
2055
_{1}})\,m_{5}\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}}
2056
\\ &&\quad\mbox{} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{5}\,r_{2}\,\cos(
2057
{\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{1}\,\sin({\theta_{1}})\,m_{5}\,r
2058
_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}} \\ &&\quad\mbox{} + 4\,r_{1
2059
}\,\sin({\theta_{1}})\,m_{4}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^
2060
2 + 4\,r_{1}\,\sin({\theta_{1}})\,m_{4}\,r_{3}\,\sin({\theta_{3}})\,{
2061
\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{4
2062
}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{1}\,\sin({\theta
2063
_{1}})\,m_{4}\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}}
2064
\\ &&\quad\mbox{} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{5}\,r_{3}\,\sin(
2065
{\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{1}\,\cos({\theta_{1}})\,m_{5}\,r
2066
_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,r_{1
2067
}\,\sin({\theta_{1}})\,m_{7}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^
2068
2 + 4\,r_{1}\,\sin({\theta_{1}})\,m_{7}\,r_{3}\,\sin({\theta_{3}})\,{
2069
\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,r_{1}\,\sin({\theta_{1}})\,m_{7
2070
}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{1}\,\sin({\theta
2071
_{1}})\,m_{7}\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}} + 2\,r_{1}
2072
\,\cos({\theta_{1}})\,m_{9}\,g \\ &&\quad\mbox{} + 4\,r_{1}\,\sin({
2073
\theta_{1}})\,m_{10}\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}} + 4
2074
\,r_{1}\,\sin({\theta_{1}})\,m_{10}\,r_{3}\,\cos({\theta_{3}})\,{{\eta
2075
_{3}}}^2 \\ &&\quad\mbox{} - 4\,r_{1}\,\cos({\theta_{1}})\,m_{8}\,r_{3
2076
}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2 + 4\,r_{1}\,\sin({\theta_{1}})\,
2077
m_{7}\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}} \\ &&\quad\mbox{}
2078
- 4\,r_{1}\,\cos({\theta_{1}})\,m_{5}\,r_{2}\,\sin({\theta_{2}})\,{{
2079
\eta_{2}}}^2 - 4\,r_{1}\,\cos({\theta_{1}})\,m_{7}\,r_{5}\,\sin({
2080
\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{} + 4\,r_{1}\,\cos({
2081
\theta_{1}})\,m_{10}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}} - 4
2082
\,r_{1}\,\cos({\theta_{1}})\,m_{10}\,r_{4}\,\sin({\theta_{4}})\,{{\eta
2083
_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{1}\,\cos({\theta_{1}})\,m_{10}\,r_{
2084
4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}} + 2\,r_{1}\,\cos({\theta_{1}}
2085
)\,m_{2}\,g + 2\,r_{1}\,\cos({\theta_{1}})\,m_{4}\,g + 2\,r_{1}\,\cos(
2086
{\theta_{1}})\,m_{3}\,g \\ &&\quad\mbox{} + 2\,r_{1}\,\cos({\theta_{1}
2087
})\,m_{8}\,g + 2\,r_{1}\,\cos({\theta_{1}})\,m_{7}\,g + 2\,r_{1}\,\cos
2088
({\theta_{1}})\,m_{6}\,g + 2\,r_{1}\,\cos({\theta_{1}})\,m_{5}\,g + 2
2089
\,r_{1}\,\cos({\theta_{1}})\,m_{10}\,g \\ &&\quad\mbox{} + J_{1}\,{
2090
\dot{\eta}_{1}} + 2\,r_{1}\,\sin({\theta_{1}})\,m_{8}\,r_{8}\,\sin({
2091
\theta_{8}})\,{\dot{\eta}_{8}} + 2\,r_{1}\,\cos({\theta_{1}})\,m_{8}\,
2092
r_{8}\,\cos({\theta_{8}})\,{\dot{\eta}_{8}} \\ &&\quad\mbox{} + 2\,r_{
2093
1}\,\sin({\theta_{1}})\,m_{9}\,r_{9}\,\sin({\theta_{9}})\,{\dot{\eta}
2094
_{9}} + 2\,r_{1}\,\cos({\theta_{1}})\,m_{9}\,r_{9}\,\cos({\theta_{9}})
2095
\,{\dot{\eta}_{9}} \\ &&\quad\mbox{} + 2\,r_{1}\,\cos({\theta_{1}})\,m
2096
_{10}\,r_{10}\,\cos({\theta_{10}})\,{\dot{\eta}_{10}} + 2\,r_{1}\,\sin
2097
({\theta_{1}})\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,{\dot{\eta}_{10}}
2098
\\ &&\quad\mbox{} + m_{1}\,{r_{1}}^2\,{\dot{\eta}_{1}} + 2\,r_{1}\,
2099
\cos({\theta_{1}})\,m_{2}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}}
2100
+ 2\,r_{1}\,\sin({\theta_{1}})\,m_{2}\,r_{2}\,\sin({\theta_{2}})\,{
2101
\dot{\eta}_{2}} \\ &&\quad\mbox{} + 2\,r_{1}\,\sin({\theta_{1}})\,m_{2
2102
}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 - 2\,r_{1}\,\cos({\theta
2103
_{1}})\,m_{2}\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2
2104
\\ &&\quad\mbox{} + 2\,r_{1}\,\sin({\theta_{1}})\,m_{3}\,r_{3}\,\cos(
2105
{\theta_{3}})\,{{\eta_{3}}}^2 - 2\,r_{1}\,\cos({\theta_{1}})\,m_{3}\,r
2106
_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} - 2\,r_{1}
2107
\,\cos({\theta_{1}})\,m_{4}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^2
2108
+ 2\,r_{1}\,\sin({\theta_{1}})\,m_{4}\,r_{4}\,\cos({\theta_{4}})\,{{
2109
\eta_{4}}}^2 \\ &&\quad\mbox{} - 2\,r_{1}\,\cos({\theta_{1}})\,m_{5}\,
2110
r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2 + 2\,r_{1}\,\sin({\theta_{1}
2111
})\,m_{5}\,r_{5}\,\cos({\theta_{5}})\,{{\eta_{5}}}^2 \\ &&\quad\mbox{}
2112
+ 2\,r_{1}\,\sin({\theta_{1}})\,m_{6}\,r_{6}\,\cos({\theta_{6}})\,{{
2113
\eta_{6}}}^2 - 2\,r_{1}\,\cos({\theta_{1}})\,m_{6}\,r_{6}\,\sin({
2114
\theta_{6}})\,{{\eta_{6}}}^2 \\ &&\quad\mbox{} + 2\,r_{1}\,\sin({
2115
\theta_{1}})\,m_{7}\,r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^2 - 2\,r
2116
_{1}\,\cos({\theta_{1}})\,m_{7}\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7}
2117
}}^2 \\ &&\quad\mbox{} - 2\,r_{1}\,\cos({\theta_{1}})\,m_{8}\,r_{8}\,
2118
\sin({\theta_{8}})\,{{\eta_{8}}}^2 + 2\,r_{1}\,\sin({\theta_{1}})\,m_{
2119
8}\,r_{8}\,\cos({\theta_{8}})\,{{\eta_{8}}}^2 \\ &&\quad\mbox{} + 2\,r
2120
_{1}\,\sin({\theta_{1}})\,m_{10}\,r_{10}\,\cos({\theta_{10}})\,{{\eta
2121
_{10}}}^2 - 2\,r_{1}\,\cos({\theta_{1}})\,m_{10}\,r_{10}\,\sin({\theta
2122
_{10}})\,{{\eta_{10}}}^2 \\ &&\quad\mbox{} + 2\,r_{1}\,\sin({\theta_{1
2123
}})\,m_{3}\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}} + 2\,r_{1}\,
2124
\cos({\theta_{1}})\,m_{3}\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}}
2125
\\ &&\quad\mbox{} + 2\,r_{1}\,\cos({\theta_{1}})\,m_{4}\,r_{4}\,\cos(
2126
{\theta_{4}})\,{\dot{\eta}_{4}} + 2\,r_{1}\,\sin({\theta_{1}})\,m_{4}
2127
\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} + 2\,r
2128
_{1}\,\cos({\theta_{1}})\,m_{5}\,r_{5}\,\cos({\theta_{5}})\,{
2129
\dot{\eta}_{5}} + 2\,r_{1}\,\sin({\theta_{1}})\,m_{5}\,r_{5}\,\sin({
2130
\theta_{5}})\,{\dot{\eta}_{5}} \\ &&\quad\mbox{} + 2\,r_{1}\,\sin({
2131
\theta_{1}})\,m_{6}\,r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}_{6}} + 2\,
2132
r_{1}\,\cos({\theta_{1}})\,m_{6}\,r_{6}\,\cos({\theta_{6}})\,{
2133
\dot{\eta}_{6}} \\ &&\quad\mbox{} + 2\,r_{1}\,\sin({\theta_{1}})\,m_{7
2134
}\,r_{7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}} + 2\,r_{1}\,\cos({
2135
\theta_{1}})\,m_{7}\,r_{7}\,\cos({\theta_{7}})\,{\dot{\eta}_{7}} + 4\,
2136
{r_{1}}^2\,m_{2}\,{\dot{\eta}_{1}} \end{eqnarray*}
2137
\begin{eqnarray*} && m_{10}\,g\,r_{10}\,\cos({\theta_{10}}) + J_{10}\,
2138
{\dot{\eta}_{10}} + m_{10}\,{r_{10}}^2\,{\dot{\eta}_{10}} + 2\,m_{10}
2139
\,r_{10}\,\cos({\theta_{10}})\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}
2140
_{2}} \\ &&\quad\mbox{} + 2\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,r_{2
2141
}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 + 2\,m_{10}\,r_{10}\,\sin({
2142
\theta_{10}})\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}}
2143
\\ &&\quad\mbox{} + 2\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,r_{5}\,
2144
\cos({\theta_{5}})\,{{\eta_{5}}}^2 + 2\,m_{10}\,r_{10}\,\sin({\theta_{
2145
10}})\,r_{5}\,\sin({\theta_{5}})\,{\dot{\eta}_{5}} \\ &&\quad\mbox{}
2146
+ 2\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,r_{9}\,\cos({\theta_{9}})\,
2147
{{\eta_{9}}}^2 + 2\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,r_{9}\,\sin({
2148
\theta_{9}})\,{\dot{\eta}_{9}} \\ &&\quad\mbox{} + 2\,m_{10}\,r_{10}\,
2149
\sin({\theta_{10}})\,r_{8}\,\cos({\theta_{8}})\,{{\eta_{8}}}^2 + 2\,m
2150
_{10}\,r_{10}\,\sin({\theta_{10}})\,r_{8}\,\sin({\theta_{8}})\,{
2151
\dot{\eta}_{8}} \\ &&\quad\mbox{} + 2\,m_{10}\,r_{10}\,\sin({\theta_{
2152
10}})\,r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^2 + 2\,m_{10}\,r_{10}\,
2153
\sin({\theta_{10}})\,r_{7}\,\sin({\theta_{7}})\,{\dot{\eta}_{7}}
2154
\\ &&\quad\mbox{} + 2\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,r_{6}\,
2155
\cos({\theta_{6}})\,{{\eta_{6}}}^2 + 2\,m_{10}\,r_{10}\,\sin({\theta_{
2156
10}})\,r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}_{6}} \\ &&\quad\mbox{}
2157
- 2\,m_{10}\,r_{10}\,\cos({\theta_{10}})\,r_{1}\,\sin({\theta_{1}})\,
2158
{{\eta_{1}}}^2 + 2\,m_{10}\,r_{10}\,\cos({\theta_{10}})\,r_{1}\,\cos({
2159
\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} - 2\,m_{10}\,r_{10}\,
2160
\cos({\theta_{10}})\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2 + 2\,m
2161
_{10}\,r_{10}\,\cos({\theta_{10}})\,r_{4}\,\cos({\theta_{4}})\,{
2162
\dot{\eta}_{4}} \\ &&\quad\mbox{} - 2\,m_{10}\,r_{10}\,\cos({\theta_{
2163
10}})\,r_{5}\,\sin({\theta_{5}})\,{{\eta_{5}}}^2 + 2\,m_{10}\,r_{10}\,
2164
\cos({\theta_{10}})\,r_{5}\,\cos({\theta_{5}})\,{\dot{\eta}_{5}}
2165
\\ &&\quad\mbox{} - 2\,m_{10}\,r_{10}\,\cos({\theta_{10}})\,r_{8}\,
2166
\sin({\theta_{8}})\,{{\eta_{8}}}^2 + 2\,m_{10}\,r_{10}\,\cos({\theta_{
2167
10}})\,r_{8}\,\cos({\theta_{8}})\,{\dot{\eta}_{8}} \\ &&\quad\mbox{}
2168
- 2\,m_{10}\,r_{10}\,\cos({\theta_{10}})\,r_{9}\,\sin({\theta_{9}})\,
2169
{{\eta_{9}}}^2 + 2\,m_{10}\,r_{10}\,\cos({\theta_{10}})\,r_{9}\,\cos({
2170
\theta_{9}})\,{\dot{\eta}_{9}} \\ &&\quad\mbox{} - 2\,m_{10}\,r_{10}\,
2171
\cos({\theta_{10}})\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7}}}^2 + 2\,m
2172
_{10}\,r_{10}\,\cos({\theta_{10}})\,r_{7}\,\cos({\theta_{7}})\,{
2173
\dot{\eta}_{7}} \\ &&\quad\mbox{} - 2\,m_{10}\,r_{10}\,\cos({\theta_{
2174
10}})\,r_{6}\,\sin({\theta_{6}})\,{{\eta_{6}}}^2 + 2\,m_{10}\,r_{10}\,
2175
\cos({\theta_{10}})\,r_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}}
2176
\\ &&\quad\mbox{} + 2\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,r_{1}\,
2177
\cos({\theta_{1}})\,{{\eta_{1}}}^2 + 2\,m_{10}\,r_{10}\,\sin({\theta_{
2178
10}})\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{}
2179
+ 2\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,r_{4}\,\cos({\theta_{4}})\,
2180
{{\eta_{4}}}^2 + 2\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,r_{4}\,\sin({
2181
\theta_{4}})\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} + 2\,m_{10}\,r_{10}\,
2182
\sin({\theta_{10}})\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2 - 2\,m
2183
_{10}\,r_{10}\,\cos({\theta_{10}})\,r_{4}\,\sin({\theta_{4}})\,{{\eta
2184
_{4}}}^2 \\ &&\quad\mbox{} + 2\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,r
2185
_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}} + 2\,m_{10}\,r_{10}\,\cos({
2186
\theta_{10}})\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}}
2187
\\ &&\quad\mbox{} - 2\,m_{10}\,r_{10}\,\cos({\theta_{10}})\,r_{2}\,
2188
\sin({\theta_{2}})\,{{\eta_{2}}}^2 \end{eqnarray*}
2189
\begin{eqnarray*} && m_{5}\,g\,r_{5}\,\cos({\theta_{5}}) + 2\,r_{5}\,
2190
\cos({\theta_{5}})\,m_{10}\,g + 2\,r_{5}\,\cos({\theta_{5}})\,m_{7}\,g
2191
+ 2\,r_{5}\,\cos({\theta_{5}})\,m_{8}\,g + 2\,r_{5}\,\cos({\theta_{5}
2192
})\,m_{9}\,g \\ &&\quad\mbox{} + 2\,r_{5}\,\cos({\theta_{5}})\,m_{6}\,
2193
g + 4\,{r_{5}}^2\,m_{7}\,{\dot{\eta}_{5}} + 4\,{r_{5}}^2\,m_{6}\,{
2194
\dot{\eta}_{5}} + 4\,{r_{5}}^2\,m_{8}\,{\dot{\eta}_{5}} + 4\,{r_{5}}^2
2195
\,m_{9}\,{\dot{\eta}_{5}} \\ &&\quad\mbox{} + 4\,{r_{5}}^2\,m_{10}\,{
2196
\dot{\eta}_{5}} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{7}\,r_{3}\,\sin({
2197
\theta_{3}})\,{\dot{\eta}_{3}} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{7}\,
2198
r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{5}
2199
\,\sin({\theta_{5}})\,m_{7}\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2
2200
}} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{7}\,r_{4}\,\sin({\theta_{4}})\,{
2201
\dot{\eta}_{4}} \\ &&\quad\mbox{} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{7
2202
}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2 + 4\,r_{5}\,\sin({\theta
2203
_{5}})\,m_{7}\,r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}_{6}}
2204
\\ &&\quad\mbox{} + 4\,r_{5}\,\cos({\theta_{5}})\,m_{6}\,r_{1}\,\cos(
2205
{\theta_{1}})\,{\dot{\eta}_{1}} - 4\,r_{5}\,\cos({\theta_{5}})\,m_{6}
2206
\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} + 4\,r_{
2207
5}\,\cos({\theta_{5}})\,m_{6}\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}
2208
_{3}} - 4\,r_{5}\,\cos({\theta_{5}})\,m_{6}\,r_{2}\,\sin({\theta_{2}})
2209
\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{5}\,\cos({\theta_{5}})\,m_{
2210
6}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}} - 4\,r_{5}\,\cos({
2211
\theta_{5}})\,m_{6}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^2
2212
\\ &&\quad\mbox{} + 4\,r_{5}\,\cos({\theta_{5}})\,m_{6}\,r_{4}\,\cos(
2213
{\theta_{4}})\,{\dot{\eta}_{4}} - 4\,r_{5}\,\cos({\theta_{5}})\,m_{6}
2214
\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{
2215
5}\,\sin({\theta_{5}})\,m_{7}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}
2216
^2 - 4\,r_{5}\,\cos({\theta_{5}})\,m_{7}\,r_{6}\,\sin({\theta_{6}})\,{
2217
{\eta_{6}}}^2 \\ &&\quad\mbox{} + 4\,r_{5}\,\cos({\theta_{5}})\,m_{7}
2218
\,r_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}} + 4\,r_{5}\,\cos({\theta
2219
_{5}})\,m_{8}\,r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}}
2220
\\ &&\quad\mbox{} - 4\,r_{5}\,\cos({\theta_{5}})\,m_{8}\,r_{2}\,\sin(
2221
{\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{5}\,\sin({\theta_{5}})\,m_{6}\,r
2222
_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} - 4\,r_{5
2223
}\,\cos({\theta_{5}})\,m_{8}\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^
2224
2 + 4\,r_{5}\,\sin({\theta_{5}})\,m_{6}\,r_{4}\,\cos({\theta_{4}})\,{{
2225
\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{6}\,
2226
r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}} + 4\,r_{5}\,\sin({\theta_{
2227
5}})\,m_{6}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2
2228
\\ &&\quad\mbox{} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{6}\,r_{1}\,\cos(
2229
{\theta_{1}})\,{{\eta_{1}}}^2 + 4\,r_{5}\,\sin({\theta_{5}})\,m_{6}\,r
2230
_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}} \\ &&\quad\mbox{} + 4\,r_{5
2231
}\,\sin({\theta_{5}})\,m_{6}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^
2232
2 + 4\,r_{5}\,\sin({\theta_{5}})\,m_{6}\,r_{2}\,\sin({\theta_{2}})\,{
2233
\dot{\eta}_{2}} \\ &&\quad\mbox{} - 4\,r_{5}\,\cos({\theta_{5}})\,m_{8
2234
}\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}^2 + 2\,m_{5}\,r_{5}\,\sin({
2235
\theta_{5}})\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}}
2236
\\ &&\quad\mbox{} + 2\,m_{5}\,r_{5}\,\sin({\theta_{5}})\,r_{2}\,\cos(
2237
{\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{5}\,\cos({\theta_{5}})\,m_{8}\,r
2238
_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} - 4\,r_{5
2239
}\,\cos({\theta_{5}})\,m_{8}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^
2240
2 + 4\,r_{5}\,\cos({\theta_{5}})\,m_{8}\,r_{4}\,\cos({\theta_{4}})\,{
2241
\dot{\eta}_{4}} \\ &&\quad\mbox{} - 4\,r_{5}\,\cos({\theta_{5}})\,m_{8
2242
}\,r_{7}\,\sin({\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{5}\,\cos({\theta
2243
_{5}})\,m_{8}\,r_{7}\,\cos({\theta_{7}})\,{\dot{\eta}_{7}}
2244
\\ &&\quad\mbox{} + 4\,r_{5}\,\cos({\theta_{5}})\,m_{8}\,r_{2}\,\cos(
2245
{\theta_{2}})\,{\dot{\eta}_{2}} - 4\,r_{5}\,\cos({\theta_{5}})\,m_{8}
2246
\,r_{6}\,\sin({\theta_{6}})\,{{\eta_{6}}}^2 \\ &&\quad\mbox{} + 4\,r_{
2247
5}\,\cos({\theta_{5}})\,m_{8}\,r_{1}\,\cos({\theta_{1}})\,{\dot{\eta}
2248
_{1}} - 4\,r_{5}\,\cos({\theta_{5}})\,m_{10}\,r_{2}\,\sin({\theta_{2}}
2249
)\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{5}\,\cos({\theta_{5}})\,m
2250
_{10}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}_{2}} - 4\,r_{5}\,\cos({
2251
\theta_{5}})\,m_{10}\,r_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^2
2252
\\ &&\quad\mbox{} + 4\,r_{5}\,\cos({\theta_{5}})\,m_{10}\,r_{3}\,\cos
2253
({\theta_{3}})\,{\dot{\eta}_{3}} + 4\,r_{5}\,\cos({\theta_{5}})\,m_{10
2254
}\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}} \\ &&\quad\mbox{} - 4\,
2255
r_{5}\,\cos({\theta_{5}})\,m_{10}\,r_{8}\,\sin({\theta_{8}})\,{{\eta_{
2256
8}}}^2 + 4\,r_{5}\,\cos({\theta_{5}})\,m_{10}\,r_{8}\,\cos({\theta_{8}
2257
})\,{\dot{\eta}_{8}} \\ &&\quad\mbox{} + 4\,r_{5}\,\sin({\theta_{5}})
2258
\,m_{10}\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2 + 4\,r_{5}\,\cos({
2259
\theta_{5}})\,m_{10}\,r_{9}\,\cos({\theta_{9}})\,{\dot{\eta}_{9}}
2260
\\ &&\quad\mbox{} - 4\,r_{5}\,\cos({\theta_{5}})\,m_{10}\,r_{7}\,\sin
2261
({\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{5}\,\cos({\theta_{5}})\,m_{10}
2262
\,r_{7}\,\cos({\theta_{7}})\,{\dot{\eta}_{7}} \\ &&\quad\mbox{} + 4\,r
2263
_{5}\,\cos({\theta_{5}})\,m_{10}\,r_{6}\,\cos({\theta_{6}})\,{
2264
\dot{\eta}_{6}} - 4\,r_{5}\,\cos({\theta_{5}})\,m_{10}\,r_{6}\,\sin({
2265
\theta_{6}})\,{{\eta_{6}}}^2 \\ &&\quad\mbox{} - 4\,r_{5}\,\cos({
2266
\theta_{5}})\,m_{10}\,r_{9}\,\sin({\theta_{9}})\,{{\eta_{9}}}^2 - 4\,r
2267
_{5}\,\cos({\theta_{5}})\,m_{10}\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1
2268
}}}^2 \\ &&\quad\mbox{} + 2\,m_{5}\,r_{5}\,\sin({\theta_{5}})\,r_{2}\,
2269
\sin({\theta_{2}})\,{\dot{\eta}_{2}} + 4\,r_{5}\,\cos({\theta_{5}})\,m
2270
_{10}\,r_{1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{}
2271
- 4\,r_{5}\,\cos({\theta_{5}})\,m_{10}\,r_{3}\,\sin({\theta_{3}})\,{{
2272
\eta_{3}}}^2 + 2\,m_{5}\,r_{5}\,\sin({\theta_{5}})\,r_{4}\,\cos({
2273
\theta_{4}})\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 2\,m_{5}\,r_{5}\,\sin
2274
({\theta_{5}})\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}} + 2\,m_{5}
2275
\,r_{5}\,\sin({\theta_{5}})\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2
2276
\\ &&\quad\mbox{} + 4\,r_{5}\,\cos({\theta_{5}})\,m_{9}\,r_{4}\,\cos(
2277
{\theta_{4}})\,{\dot{\eta}_{4}} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{10}
2278
\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} + 4\,r
2279
_{5}\,\sin({\theta_{5}})\,m_{10}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4
2280
}}}^2 - 4\,r_{5}\,\cos({\theta_{5}})\,m_{9}\,r_{4}\,\sin({\theta_{4}})
2281
\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{
2282
10}\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4}} + 4\,r_{5}\,\sin({
2283
\theta_{5}})\,m_{10}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2
2284
\\ &&\quad\mbox{} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{10}\,r_{3}\,\sin
2285
({\theta_{3}})\,{\dot{\eta}_{3}} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{10
2286
}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r
2287
_{5}\,\sin({\theta_{5}})\,m_{10}\,r_{2}\,\sin({\theta_{2}})\,{
2288
\dot{\eta}_{2}} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{10}\,r_{6}\,\cos({
2289
\theta_{6}})\,{{\eta_{6}}}^2 \\ &&\quad\mbox{} + 4\,r_{5}\,\sin({
2290
\theta_{5}})\,m_{10}\,r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}_{6}} + 4
2291
\,r_{5}\,\sin({\theta_{5}})\,m_{10}\,r_{9}\,\cos({\theta_{9}})\,{{\eta
2292
_{9}}}^2 \\ &&\quad\mbox{} + 4\,r_{5}\,\cos({\theta_{5}})\,m_{9}\,r_{3
2293
}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}} - 4\,r_{5}\,\cos({\theta_{5}})
2294
\,m_{9}\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{}
2295
+ 4\,r_{5}\,\cos({\theta_{5}})\,m_{9}\,r_{2}\,\cos({\theta_{2}})\,{
2296
\dot{\eta}_{2}} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{10}\,r_{8}\,\sin({
2297
\theta_{8}})\,{\dot{\eta}_{8}} \\ &&\quad\mbox{} + 4\,r_{5}\,\sin({
2298
\theta_{5}})\,m_{10}\,r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r
2299
_{5}\,\sin({\theta_{5}})\,m_{10}\,r_{7}\,\sin({\theta_{7}})\,{
2300
\dot{\eta}_{7}} \\ &&\quad\mbox{} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{9
2301
}\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 + 4\,r_{5}\,\sin({\theta
2302
_{5}})\,m_{9}\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}}
2303
\\ &&\quad\mbox{} - 4\,r_{5}\,\cos({\theta_{5}})\,m_{9}\,r_{1}\,\sin(
2304
{\theta_{1}})\,{{\eta_{1}}}^2 + 4\,r_{5}\,\sin({\theta_{5}})\,m_{9}\,r
2305
_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{5}
2306
\,\sin({\theta_{5}})\,m_{9}\,r_{4}\,\sin({\theta_{4}})\,{\dot{\eta}_{4
2307
}} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{9}\,r_{3}\,\cos({\theta_{3}})\,{
2308
{\eta_{3}}}^2 \\ &&\quad\mbox{} - 4\,r_{5}\,\cos({\theta_{5}})\,m_{9}
2309
\,r_{6}\,\sin({\theta_{6}})\,{{\eta_{6}}}^2 + 4\,r_{5}\,\sin({\theta_{
2310
5}})\,m_{9}\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}}
2311
\\ &&\quad\mbox{} + 4\,r_{5}\,\cos({\theta_{5}})\,m_{9}\,r_{1}\,\cos(
2312
{\theta_{1}})\,{\dot{\eta}_{1}} - 4\,r_{5}\,\cos({\theta_{5}})\,m_{9}
2313
\,r_{3}\,\sin({\theta_{3}})\,{{\eta_{3}}}^2 \\ &&\quad\mbox{} + 4\,r_{
2314
5}\,\sin({\theta_{5}})\,m_{10}\,r_{9}\,\sin({\theta_{9}})\,{\dot{\eta}
2315
_{9}} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{10}\,r_{8}\,\cos({\theta_{8}}
2316
)\,{{\eta_{8}}}^2 \\ &&\quad\mbox{} + 4\,r_{5}\,\cos({\theta_{5}})\,m
2317
_{9}\,r_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}} + 4\,r_{5}\,\cos({
2318
\theta_{5}})\,m_{9}\,r_{8}\,\cos({\theta_{8}})\,{\dot{\eta}_{8}}
2319
\\ &&\quad\mbox{} - 4\,r_{5}\,\cos({\theta_{5}})\,m_{9}\,r_{7}\,\sin(
2320
{\theta_{7}})\,{{\eta_{7}}}^2 + 4\,r_{5}\,\cos({\theta_{5}})\,m_{9}\,r
2321
_{7}\,\cos({\theta_{7}})\,{\dot{\eta}_{7}} \\ &&\quad\mbox{} - 4\,r_{5
2322
}\,\cos({\theta_{5}})\,m_{9}\,r_{8}\,\sin({\theta_{8}})\,{{\eta_{8}}}^
2323
2 + 4\,r_{5}\,\sin({\theta_{5}})\,m_{9}\,r_{8}\,\cos({\theta_{8}})\,{{
2324
\eta_{8}}}^2 \\ &&\quad\mbox{} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{9}\,
2325
r_{6}\,\sin({\theta_{6}})\,{\dot{\eta}_{6}} + 4\,r_{5}\,\sin({\theta_{
2326
5}})\,m_{8}\,r_{3}\,\cos({\theta_{3}})\,{{\eta_{3}}}^2
2327
\\ &&\quad\mbox{} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{8}\,r_{6}\,\sin(
2328
{\theta_{6}})\,{\dot{\eta}_{6}} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{9}
2329
\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2 \\ &&\quad\mbox{} - 4\,r_{
2330
5}\,\cos({\theta_{5}})\,m_{7}\,r_{1}\,\sin({\theta_{1}})\,{{\eta_{1}}}
2331
^2 + 4\,r_{5}\,\cos({\theta_{5}})\,m_{7}\,r_{1}\,\cos({\theta_{1}})\,{
2332
\dot{\eta}_{1}} \\ &&\quad\mbox{} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{9
2333
}\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} + 4\,r_{5}\,\sin({
2334
\theta_{5}})\,m_{9}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^2
2335
\\ &&\quad\mbox{} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{8}\,r_{4}\,\sin(
2336
{\theta_{4}})\,{\dot{\eta}_{4}} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{9}
2337
\,r_{8}\,\sin({\theta_{8}})\,{\dot{\eta}_{8}} \\ &&\quad\mbox{} + 4\,r
2338
_{5}\,\sin({\theta_{5}})\,m_{9}\,r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}
2339
}}^2 + 4\,r_{5}\,\sin({\theta_{5}})\,m_{9}\,r_{7}\,\sin({\theta_{7}})
2340
\,{\dot{\eta}_{7}} \\ &&\quad\mbox{} + 4\,r_{5}\,\sin({\theta_{5}})\,m
2341
_{8}\,r_{2}\,\sin({\theta_{2}})\,{\dot{\eta}_{2}} + 4\,r_{5}\,\sin({
2342
\theta_{5}})\,m_{8}\,r_{7}\,\cos({\theta_{7}})\,{{\eta_{7}}}^2
2343
\\ &&\quad\mbox{} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{8}\,r_{7}\,\sin(
2344
{\theta_{7}})\,{\dot{\eta}_{7}} - 4\,r_{5}\,\cos({\theta_{5}})\,m_{7}
2345
\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{
2346
5}\,\cos({\theta_{5}})\,m_{7}\,r_{2}\,\cos({\theta_{2}})\,{\dot{\eta}
2347
_{2}} - 4\,r_{5}\,\cos({\theta_{5}})\,m_{7}\,r_{4}\,\sin({\theta_{4}})
2348
\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 4\,r_{5}\,\cos({\theta_{5}})\,m_{
2349
7}\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4}} + 4\,r_{5}\,\sin({
2350
\theta_{5}})\,m_{8}\,r_{3}\,\sin({\theta_{3}})\,{\dot{\eta}_{3}}
2351
\\ &&\quad\mbox{} + 4\,r_{5}\,\cos({\theta_{5}})\,m_{7}\,r_{3}\,\cos(
2352
{\theta_{3}})\,{\dot{\eta}_{3}} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{8}
2353
\,r_{2}\,\cos({\theta_{2}})\,{{\eta_{2}}}^2 \\ &&\quad\mbox{} + 4\,r_{
2354
5}\,\sin({\theta_{5}})\,m_{8}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}
2355
^2 + 4\,r_{5}\,\sin({\theta_{5}})\,m_{8}\,r_{1}\,\cos({\theta_{1}})\,{
2356
{\eta_{1}}}^2 \\ &&\quad\mbox{} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{8}
2357
\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} + 4\,r_{5}\,\sin({\theta
2358
_{5}})\,m_{8}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^2
2359
\\ &&\quad\mbox{} + 4\,r_{5}\,\sin({\theta_{5}})\,m_{7}\,r_{1}\,\cos(
2360
{\theta_{1}})\,{{\eta_{1}}}^2 + 4\,r_{5}\,\sin({\theta_{5}})\,m_{7}\,r
2361
_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}} \\ &&\quad\mbox{} + 4\,r_{5
2362
}\,\sin({\theta_{5}})\,m_{7}\,r_{4}\,\cos({\theta_{4}})\,{{\eta_{4}}}^
2363
2 - 4\,r_{5}\,\cos({\theta_{5}})\,m_{7}\,r_{3}\,\sin({\theta_{3}})\,{{
2364
\eta_{3}}}^2 \\ &&\quad\mbox{} + 2\,m_{5}\,r_{5}\,\cos({\theta_{5}})\,
2365
r_{3}\,\cos({\theta_{3}})\,{\dot{\eta}_{3}} - 2\,m_{5}\,r_{5}\,\cos({
2366
\theta_{5}})\,r_{2}\,\sin({\theta_{2}})\,{{\eta_{2}}}^2
2367
\\ &&\quad\mbox{} - 2\,m_{5}\,r_{5}\,\cos({\theta_{5}})\,r_{3}\,\sin(
2368
{\theta_{3}})\,{{\eta_{3}}}^2 - 2\,m_{5}\,r_{5}\,\cos({\theta_{5}})\,r
2369
_{4}\,\sin({\theta_{4}})\,{{\eta_{4}}}^2 \\ &&\quad\mbox{} + 2\,m_{5}
2370
\,r_{5}\,\cos({\theta_{5}})\,r_{4}\,\cos({\theta_{4}})\,{\dot{\eta}_{4
2371
}} + 2\,m_{5}\,r_{5}\,\cos({\theta_{5}})\,r_{2}\,\cos({\theta_{2}})\,{
2372
\dot{\eta}_{2}} \\ &&\quad\mbox{} + 2\,m_{5}\,r_{5}\,\sin({\theta_{5}}
2373
)\,r_{1}\,\cos({\theta_{1}})\,{{\eta_{1}}}^2 + 2\,m_{5}\,r_{5}\,\sin({
2374
\theta_{5}})\,r_{1}\,\sin({\theta_{1}})\,{\dot{\eta}_{1}}
2375
\\ &&\quad\mbox{} - 2\,m_{5}\,r_{5}\,\cos({\theta_{5}})\,r_{1}\,\sin(
2376
{\theta_{1}})\,{{\eta_{1}}}^2 + 2\,m_{5}\,r_{5}\,\cos({\theta_{5}})\,r
2377
_{1}\,\cos({\theta_{1}})\,{\dot{\eta}_{1}} + J_{5}\,{\dot{\eta}_{5}}
2378
\\ &&\quad\mbox{} + 2\,r_{5}\,\sin({\theta_{5}})\,m_{8}\,r_{8}\,\sin(
2379
{\theta_{8}})\,{\dot{\eta}_{8}} + 2\,r_{5}\,\cos({\theta_{5}})\,m_{8}
2380
\,r_{8}\,\cos({\theta_{8}})\,{\dot{\eta}_{8}} \\ &&\quad\mbox{} + 2\,r
2381
_{5}\,\sin({\theta_{5}})\,m_{9}\,r_{9}\,\sin({\theta_{9}})\,{
2382
\dot{\eta}_{9}} + 2\,r_{5}\,\cos({\theta_{5}})\,m_{9}\,r_{9}\,\cos({
2383
\theta_{9}})\,{\dot{\eta}_{9}} \\ &&\quad\mbox{} + 2\,r_{5}\,\cos({
2384
\theta_{5}})\,m_{10}\,r_{10}\,\cos({\theta_{10}})\,{\dot{\eta}_{10}}
2385
+ 2\,r_{5}\,\sin({\theta_{5}})\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,
2386
{\dot{\eta}_{10}} \\ &&\quad\mbox{} + 2\,r_{5}\,\sin({\theta_{5}})\,m
2387
_{6}\,r_{6}\,\cos({\theta_{6}})\,{{\eta_{6}}}^2 - 2\,r_{5}\,\cos({
2388
\theta_{5}})\,m_{6}\,r_{6}\,\sin({\theta_{6}})\,{{\eta_{6}}}^2
2389
\\ &&\quad\mbox{} + 2\,r_{5}\,\sin({\theta_{5}})\,m_{7}\,r_{7}\,\cos(
2390
{\theta_{7}})\,{{\eta_{7}}}^2 - 2\,r_{5}\,\cos({\theta_{5}})\,m_{7}\,r
2391
_{7}\,\sin({\theta_{7}})\,{{\eta_{7}}}^2 \\ &&\quad\mbox{} + 2\,r_{5}
2392
\,\sin({\theta_{5}})\,m_{8}\,r_{8}\,\cos({\theta_{8}})\,{{\eta_{8}}}^2
2393
- 2\,r_{5}\,\cos({\theta_{5}})\,m_{8}\,r_{8}\,\sin({\theta_{8}})\,{{
2394
\eta_{8}}}^2 \\ &&\quad\mbox{} + 2\,r_{5}\,\sin({\theta_{5}})\,m_{9}\,
2395
r_{9}\,\cos({\theta_{9}})\,{{\eta_{9}}}^2 - 2\,r_{5}\,\cos({\theta_{5}
2396
})\,m_{9}\,r_{9}\,\sin({\theta_{9}})\,{{\eta_{9}}}^2 \\ &&\quad\mbox{}
2397
- 2\,r_{5}\,\cos({\theta_{5}})\,m_{10}\,r_{10}\,\sin({\theta_{10}})\,
2398
{{\eta_{10}}}^2 + 2\,r_{5}\,\sin({\theta_{5}})\,m_{10}\,r_{10}\,\cos({
2399
\theta_{10}})\,{{\eta_{10}}}^2 + m_{5}\,{r_{5}}^2\,{\dot{\eta}_{5}}
2400
\\ &&\quad\mbox{} + 2\,r_{5}\,\sin({\theta_{5}})\,m_{6}\,r_{6}\,\sin(
2401
{\theta_{6}})\,{\dot{\eta}_{6}} + 2\,r_{5}\,\cos({\theta_{5}})\,m_{6}
2402
\,r_{6}\,\cos({\theta_{6}})\,{\dot{\eta}_{6}} \\ &&\quad\mbox{} + 2\,r
2403
_{5}\,\cos({\theta_{5}})\,m_{7}\,r_{7}\,\cos({\theta_{7}})\,{
2404
\dot{\eta}_{7}} + 2\,r_{5}\,\sin({\theta_{5}})\,m_{7}\,r_{7}\,\sin({
2405
\theta_{7}})\,{\dot{\eta}_{7}} \end{eqnarray*}
2406
a cononical form $M(q)\dot{t}+C(q)t^2 +R$,M:
2408
$$ \left( \begin{array}{cccccccccc} 4\,{r_{1}}^2\,m_{8}+4\,{r_{1}}^2\,
2409
m_{10}+m_{1}\,{r_{1}}^2+4\,{r_{1}}^2\,m_{6}+4\,{r_{1}}^2\,m_{9}+4\,{r
2410
_{1}}^2\,m_{7}+4\,{r_{1}}^2\,m_{2}+J_{1}+4\,{r_{1}}^2\,m_{5}+4\,{r_{1}
2411
}^2\,m_{4}+4\,{r_{1}}^2\,m_{3} & 2\,r_{1}\,r_{2}\,\cos({\theta_{1}}-{
2412
\theta_{2}})\,(2\,m_{3}+m_{2}+2\,m_{4}+2\,m_{7}+2\,m_{10}+2\,m_{5}+2\,
2413
m_{6}+2\,m_{9}+2\,m_{8}) & 2\,r_{1}\,r_{3}\,\cos({\theta_{1}}-{\theta
2414
_{3}})\,(2\,m_{5}+2\,m_{4}+2\,m_{10}+2\,m_{8}+2\,m_{7}+m_{3}+2\,m_{9}+
2415
2\,m_{6}) & 2\,r_{1}\,r_{4}\,\cos({\theta_{1}}-{\theta_{4}})\,(2\,m_{8
2416
}+m_{4}+2\,m_{9}+2\,m_{5}+2\,m_{7}+2\,m_{10}+2\,m_{6}) & 2\,r_{1}\,r_{
2417
5}\,\cos({\theta_{1}}-{\theta_{5}})\,(2\,m_{6}+2\,m_{8}+2\,m_{9}+2\,m
2418
_{7}+m_{5}+2\,m_{10}) & 2\,r_{1}\,r_{6}\,\cos({\theta_{1}}-{\theta_{6}
2419
})\,(m_{6}+2\,m_{9}+2\,m_{10}+2\,m_{7}+2\,m_{8}) & 2\,r_{1}\,r_{7}\,
2420
\cos({\theta_{1}}-{\theta_{7}})\,(2\,m_{10}+m_{7}+2\,m_{8}+2\,m_{9})
2421
& 2\,r_{1}\,r_{8}\,\cos({\theta_{1}}-{\theta_{8}})\,(m_{8}+2\,m_{10}+
2422
2\,m_{9}) & 2\,r_{1}\,r_{9}\,\cos({\theta_{1}}-{\theta_{9}})\,(m_{9}+2
2423
\,m_{10}) & 2\,r_{1}\,m_{10}\,r_{10}\,\cos({\theta_{1}}-{\theta_{10}})
2424
\cr 2\,r_{1}\,r_{2}\,\cos({\theta_{1}}-{\theta_{2}})\,(2\,m_{3}+m_{2}
2425
+2\,m_{4}+2\,m_{7}+2\,m_{10}+2\,m_{5}+2\,m_{6}+2\,m_{9}+2\,m_{8}) & J
2426
_{2}+4\,{r_{2}}^2\,m_{3}+4\,{r_{2}}^2\,m_{4}+4\,{r_{2}}^2\,m_{7}+4\,{r
2427
_{2}}^2\,m_{8}+m_{2}\,{r_{2}}^2+4\,{r_{2}}^2\,m_{9}+4\,{r_{2}}^2\,m_{5
2428
}+4\,{r_{2}}^2\,m_{10}+4\,{r_{2}}^2\,m_{6} & 2\,r_{2}\,r_{3}\,\cos({
2429
\theta_{2}}-{\theta_{3}})\,(2\,m_{5}+2\,m_{4}+2\,m_{10}+2\,m_{8}+2\,m
2430
_{7}+m_{3}+2\,m_{9}+2\,m_{6}) & 2\,r_{2}\,r_{4}\,\cos({\theta_{2}}-{
2431
\theta_{4}})\,(2\,m_{8}+m_{4}+2\,m_{9}+2\,m_{5}+2\,m_{7}+2\,m_{10}+2\,
2432
m_{6}) & 2\,r_{2}\,r_{5}\,\cos({\theta_{2}}-{\theta_{5}})\,(2\,m_{6}+2
2433
\,m_{8}+2\,m_{9}+2\,m_{7}+m_{5}+2\,m_{10}) & 2\,r_{2}\,r_{6}\,\cos({
2434
\theta_{2}}-{\theta_{6}})\,(m_{6}+2\,m_{9}+2\,m_{10}+2\,m_{7}+2\,m_{8}
2435
) & 2\,r_{2}\,r_{7}\,\cos({\theta_{2}}-{\theta_{7}})\,(2\,m_{10}+m_{7}
2436
+2\,m_{8}+2\,m_{9}) & 2\,r_{2}\,r_{8}\,\cos({\theta_{2}}-{\theta_{8}})
2437
\,(m_{8}+2\,m_{10}+2\,m_{9}) & 2\,r_{2}\,r_{9}\,\cos({\theta_{2}}-{
2438
\theta_{9}})\,(m_{9}+2\,m_{10}) & 2\,r_{2}\,m_{10}\,r_{10}\,\cos({
2439
\theta_{2}}-{\theta_{10}}) \cr 2\,r_{1}\,r_{3}\,\cos({\theta_{1}}-{
2440
\theta_{3}})\,(2\,m_{5}+2\,m_{4}+2\,m_{10}+2\,m_{8}+2\,m_{7}+m_{3}+2\,
2441
m_{9}+2\,m_{6}) & 2\,r_{2}\,r_{3}\,\cos({\theta_{2}}-{\theta_{3}})\,(2
2442
\,m_{5}+2\,m_{4}+2\,m_{10}+2\,m_{8}+2\,m_{7}+m_{3}+2\,m_{9}+2\,m_{6})
2443
& 4\,{r_{3}}^2\,m_{4}+4\,{r_{3}}^2\,m_{10}+4\,{r_{3}}^2\,m_{9}+4\,{r
2444
_{3}}^2\,m_{5}+4\,{r_{3}}^2\,m_{6}+m_{3}\,{r_{3}}^2+J_{3}+4\,{r_{3}}^2
2445
\,m_{7}+4\,{r_{3}}^2\,m_{8} & 2\,r_{3}\,r_{4}\,\cos({\theta_{3}}-{
2446
\theta_{4}})\,(2\,m_{8}+m_{4}+2\,m_{9}+2\,m_{5}+2\,m_{7}+2\,m_{10}+2\,
2447
m_{6}) & 2\,r_{3}\,r_{5}\,\cos({\theta_{3}}-{\theta_{5}})\,(2\,m_{6}+2
2448
\,m_{8}+2\,m_{9}+2\,m_{7}+m_{5}+2\,m_{10}) & 2\,r_{3}\,r_{6}\,\cos({
2449
\theta_{3}}-{\theta_{6}})\,(m_{6}+2\,m_{9}+2\,m_{10}+2\,m_{7}+2\,m_{8}
2450
) & 2\,r_{3}\,r_{7}\,\cos({\theta_{3}}-{\theta_{7}})\,(2\,m_{10}+m_{7}
2451
+2\,m_{8}+2\,m_{9}) & 2\,r_{3}\,r_{8}\,\cos({\theta_{3}}-{\theta_{8}})
2452
\,(m_{8}+2\,m_{10}+2\,m_{9}) & 2\,r_{3}\,r_{9}\,\cos({\theta_{3}}-{
2453
\theta_{9}})\,(m_{9}+2\,m_{10}) & 2\,r_{3}\,m_{10}\,r_{10}\,\cos({
2454
\theta_{3}}-{\theta_{10}}) \cr 2\,r_{1}\,r_{4}\,\cos({\theta_{1}}-{
2455
\theta_{4}})\,(2\,m_{8}+m_{4}+2\,m_{9}+2\,m_{5}+2\,m_{7}+2\,m_{10}+2\,
2456
m_{6}) & 2\,r_{2}\,r_{4}\,\cos({\theta_{2}}-{\theta_{4}})\,(2\,m_{8}+m
2457
_{4}+2\,m_{9}+2\,m_{5}+2\,m_{7}+2\,m_{10}+2\,m_{6}) & 2\,r_{3}\,r_{4}
2458
\,\cos({\theta_{3}}-{\theta_{4}})\,(2\,m_{8}+m_{4}+2\,m_{9}+2\,m_{5}+2
2459
\,m_{7}+2\,m_{10}+2\,m_{6}) & 4\,{r_{4}}^2\,m_{10}+4\,{r_{4}}^2\,m_{9}
2460
+4\,{r_{4}}^2\,m_{6}+4\,{r_{4}}^2\,m_{5}+4\,{r_{4}}^2\,m_{7}+J_{4}+m_{
2461
4}\,{r_{4}}^2+4\,{r_{4}}^2\,m_{8} & 2\,r_{4}\,r_{5}\,\cos({\theta_{4}}
2462
-{\theta_{5}})\,(2\,m_{6}+2\,m_{8}+2\,m_{9}+2\,m_{7}+m_{5}+2\,m_{10})
2463
& 2\,r_{4}\,r_{6}\,\cos({\theta_{4}}-{\theta_{6}})\,(m_{6}+2\,m_{9}+2
2464
\,m_{10}+2\,m_{7}+2\,m_{8}) & 2\,r_{4}\,r_{7}\,\cos({\theta_{4}}-{
2465
\theta_{7}})\,(2\,m_{10}+m_{7}+2\,m_{8}+2\,m_{9}) & 2\,r_{4}\,r_{8}\,
2466
\cos({\theta_{4}}-{\theta_{8}})\,(m_{8}+2\,m_{10}+2\,m_{9}) & 2\,r_{4}
2467
\,r_{9}\,\cos({\theta_{4}}-{\theta_{9}})\,(m_{9}+2\,m_{10}) & 2\,r_{4}
2468
\,m_{10}\,r_{10}\,\cos({\theta_{4}}-{\theta_{10}}) \cr 2\,r_{1}\,r_{5}
2469
\,\cos({\theta_{1}}-{\theta_{5}})\,(2\,m_{6}+2\,m_{8}+2\,m_{9}+2\,m_{7
2470
}+m_{5}+2\,m_{10}) & 2\,r_{2}\,r_{5}\,\cos({\theta_{2}}-{\theta_{5}})
2471
\,(2\,m_{6}+2\,m_{8}+2\,m_{9}+2\,m_{7}+m_{5}+2\,m_{10}) & 2\,r_{3}\,r
2472
_{5}\,\cos({\theta_{3}}-{\theta_{5}})\,(2\,m_{6}+2\,m_{8}+2\,m_{9}+2\,
2473
m_{7}+m_{5}+2\,m_{10}) & 2\,r_{4}\,r_{5}\,\cos({\theta_{4}}-{\theta_{5
2474
}})\,(2\,m_{6}+2\,m_{8}+2\,m_{9}+2\,m_{7}+m_{5}+2\,m_{10}) & 4\,{r_{5}
2475
}^2\,m_{8}+4\,{r_{5}}^2\,m_{10}+4\,{r_{5}}^2\,m_{7}+4\,{r_{5}}^2\,m_{9
2476
}+4\,{r_{5}}^2\,m_{6}+J_{5}+m_{5}\,{r_{5}}^2 & 2\,r_{5}\,r_{6}\,\cos({
2477
\theta_{5}}-{\theta_{6}})\,(m_{6}+2\,m_{9}+2\,m_{10}+2\,m_{7}+2\,m_{8}
2478
) & 2\,r_{5}\,r_{7}\,\cos({\theta_{5}}-{\theta_{7}})\,(2\,m_{10}+m_{7}
2479
+2\,m_{8}+2\,m_{9}) & 2\,r_{5}\,r_{8}\,\cos({\theta_{5}}-{\theta_{8}})
2480
\,(m_{8}+2\,m_{10}+2\,m_{9}) & 2\,r_{5}\,r_{9}\,\cos({\theta_{5}}-{
2481
\theta_{9}})\,(m_{9}+2\,m_{10}) & 2\,r_{5}\,m_{10}\,r_{10}\,\cos({
2482
\theta_{5}}-{\theta_{10}}) \cr 2\,r_{1}\,r_{6}\,\cos({\theta_{1}}-{
2483
\theta_{6}})\,(m_{6}+2\,m_{9}+2\,m_{10}+2\,m_{7}+2\,m_{8}) & 2\,r_{2}
2484
\,r_{6}\,\cos({\theta_{2}}-{\theta_{6}})\,(m_{6}+2\,m_{9}+2\,m_{10}+2
2485
\,m_{7}+2\,m_{8}) & 2\,r_{3}\,r_{6}\,\cos({\theta_{3}}-{\theta_{6}})\,
2486
(m_{6}+2\,m_{9}+2\,m_{10}+2\,m_{7}+2\,m_{8}) & 2\,r_{4}\,r_{6}\,\cos({
2487
\theta_{4}}-{\theta_{6}})\,(m_{6}+2\,m_{9}+2\,m_{10}+2\,m_{7}+2\,m_{8}
2488
) & 2\,r_{5}\,r_{6}\,\cos({\theta_{5}}-{\theta_{6}})\,(m_{6}+2\,m_{9}+
2489
2\,m_{10}+2\,m_{7}+2\,m_{8}) & m_{6}\,{r_{6}}^2+4\,{r_{6}}^2\,m_{7}+4
2490
\,{r_{6}}^2\,m_{8}+J_{6}+4\,{r_{6}}^2\,m_{9}+4\,{r_{6}}^2\,m_{10} & 2
2491
\,r_{6}\,r_{7}\,\cos({\theta_{6}}-{\theta_{7}})\,(2\,m_{10}+m_{7}+2\,m
2492
_{8}+2\,m_{9}) & 2\,r_{6}\,r_{8}\,\cos({\theta_{6}}-{\theta_{8}})\,(m
2493
_{8}+2\,m_{10}+2\,m_{9}) & 2\,r_{6}\,r_{9}\,\cos({\theta_{6}}-{\theta
2494
_{9}})\,(m_{9}+2\,m_{10}) & 2\,r_{6}\,m_{10}\,r_{10}\,\cos({\theta_{6}
2495
}-{\theta_{10}}) \cr 2\,r_{1}\,r_{7}\,\cos({\theta_{1}}-{\theta_{7}})
2496
\,(2\,m_{10}+m_{7}+2\,m_{8}+2\,m_{9}) & 2\,r_{2}\,r_{7}\,\cos({\theta
2497
_{2}}-{\theta_{7}})\,(2\,m_{10}+m_{7}+2\,m_{8}+2\,m_{9}) & 2\,r_{3}\,r
2498
_{7}\,\cos({\theta_{3}}-{\theta_{7}})\,(2\,m_{10}+m_{7}+2\,m_{8}+2\,m
2499
_{9}) & 2\,r_{4}\,r_{7}\,\cos({\theta_{4}}-{\theta_{7}})\,(2\,m_{10}+m
2500
_{7}+2\,m_{8}+2\,m_{9}) & 2\,r_{5}\,r_{7}\,\cos({\theta_{5}}-{\theta_{
2501
7}})\,(2\,m_{10}+m_{7}+2\,m_{8}+2\,m_{9}) & 2\,r_{6}\,r_{7}\,\cos({
2502
\theta_{6}}-{\theta_{7}})\,(2\,m_{10}+m_{7}+2\,m_{8}+2\,m_{9}) & 4\,{r
2503
_{7}}^2\,m_{9}+4\,{r_{7}}^2\,m_{10}+4\,{r_{7}}^2\,m_{8}+J_{7}+m_{7}\,{
2504
r_{7}}^2 & 2\,r_{7}\,r_{8}\,\cos({\theta_{7}}-{\theta_{8}})\,(m_{8}+2
2505
\,m_{10}+2\,m_{9}) & 2\,r_{7}\,r_{9}\,\cos({\theta_{7}}-{\theta_{9}})
2506
\,(m_{9}+2\,m_{10}) & 2\,r_{7}\,m_{10}\,r_{10}\,\cos({\theta_{7}}-{
2507
\theta_{10}}) \cr 2\,r_{1}\,r_{8}\,\cos({\theta_{1}}-{\theta_{8}})\,(m
2508
_{8}+2\,m_{10}+2\,m_{9}) & 2\,r_{2}\,r_{8}\,\cos({\theta_{2}}-{\theta
2509
_{8}})\,(m_{8}+2\,m_{10}+2\,m_{9}) & 2\,r_{3}\,r_{8}\,\cos({\theta_{3}
2510
}-{\theta_{8}})\,(m_{8}+2\,m_{10}+2\,m_{9}) & 2\,r_{4}\,r_{8}\,\cos({
2511
\theta_{4}}-{\theta_{8}})\,(m_{8}+2\,m_{10}+2\,m_{9}) & 2\,r_{5}\,r_{8
2512
}\,\cos({\theta_{5}}-{\theta_{8}})\,(m_{8}+2\,m_{10}+2\,m_{9}) & 2\,r
2513
_{6}\,r_{8}\,\cos({\theta_{6}}-{\theta_{8}})\,(m_{8}+2\,m_{10}+2\,m_{9
2514
}) & 2\,r_{7}\,r_{8}\,\cos({\theta_{7}}-{\theta_{8}})\,(m_{8}+2\,m_{10
2515
}+2\,m_{9}) & 4\,{r_{8}}^2\,m_{9}+J_{8}+m_{8}\,{r_{8}}^2+4\,{r_{8}}^2
2516
\,m_{10} & 2\,r_{8}\,r_{9}\,\cos({\theta_{8}}-{\theta_{9}})\,(m_{9}+2
2517
\,m_{10}) & 2\,r_{8}\,m_{10}\,r_{10}\,\cos({\theta_{8}}-{\theta_{10}})
2518
\cr 2\,r_{1}\,r_{9}\,\cos({\theta_{1}}-{\theta_{9}})\,(m_{9}+2\,m_{10
2519
}) & 2\,r_{2}\,r_{9}\,\cos({\theta_{2}}-{\theta_{9}})\,(m_{9}+2\,m_{10
2520
}) & 2\,r_{3}\,r_{9}\,\cos({\theta_{3}}-{\theta_{9}})\,(m_{9}+2\,m_{10
2521
}) & 2\,r_{4}\,r_{9}\,\cos({\theta_{4}}-{\theta_{9}})\,(m_{9}+2\,m_{10
2522
}) & 2\,r_{5}\,r_{9}\,\cos({\theta_{5}}-{\theta_{9}})\,(m_{9}+2\,m_{10
2523
}) & 2\,r_{6}\,r_{9}\,\cos({\theta_{6}}-{\theta_{9}})\,(m_{9}+2\,m_{10
2524
}) & 2\,r_{7}\,r_{9}\,\cos({\theta_{7}}-{\theta_{9}})\,(m_{9}+2\,m_{10
2525
}) & 2\,r_{8}\,r_{9}\,\cos({\theta_{8}}-{\theta_{9}})\,(m_{9}+2\,m_{10
2526
}) & 4\,{r_{9}}^2\,m_{10}+J_{9}+m_{9}\,{r_{9}}^2 & 2\,r_{9}\,m_{10}\,r
2527
_{10}\,\cos({\theta_{9}}-{\theta_{10}}) \cr 2\,r_{1}\,m_{10}\,r_{10}\,
2528
\cos({\theta_{1}}-{\theta_{10}}) & 2\,r_{2}\,m_{10}\,r_{10}\,\cos({
2529
\theta_{2}}-{\theta_{10}}) & 2\,r_{3}\,m_{10}\,r_{10}\,\cos({\theta_{3
2530
}}-{\theta_{10}}) & 2\,r_{4}\,m_{10}\,r_{10}\,\cos({\theta_{4}}-{
2531
\theta_{10}}) & 2\,r_{5}\,m_{10}\,r_{10}\,\cos({\theta_{5}}-{\theta_{
2532
10}}) & 2\,r_{6}\,m_{10}\,r_{10}\,\cos({\theta_{6}}-{\theta_{10}}) & 2
2533
\,r_{7}\,m_{10}\,r_{10}\,\cos({\theta_{7}}-{\theta_{10}}) & 2\,r_{8}\,
2534
m_{10}\,r_{10}\,\cos({\theta_{8}}-{\theta_{10}}) & 2\,r_{9}\,m_{10}\,r
2535
_{10}\,\cos({\theta_{9}}-{\theta_{10}}) & m_{10}\,{r_{10}}^2+J_{10}
2536
\end{array} \right) $$
2539
$$ \left( \begin{array}{cccccccccc} 0 & 2\,r_{1}\,r_{2}\,\sin({\theta
2540
_{1}}-{\theta_{2}})\,(2\,m_{3}+m_{2}+2\,m_{4}+2\,m_{7}+2\,m_{10}+2\,m
2541
_{5}+2\,m_{6}+2\,m_{9}+2\,m_{8}) & 2\,r_{1}\,r_{3}\,\sin({\theta_{1}}-
2542
{\theta_{3}})\,(2\,m_{5}+2\,m_{4}+2\,m_{10}+2\,m_{8}+2\,m_{7}+m_{3}+2
2543
\,m_{9}+2\,m_{6}) & 2\,r_{1}\,r_{4}\,\sin({\theta_{1}}-{\theta_{4}})\,
2544
(2\,m_{8}+m_{4}+2\,m_{9}+2\,m_{5}+2\,m_{7}+2\,m_{10}+2\,m_{6}) & 2\,r
2545
_{1}\,r_{5}\,\sin({\theta_{1}}-{\theta_{5}})\,(2\,m_{6}+2\,m_{8}+2\,m
2546
_{9}+2\,m_{7}+m_{5}+2\,m_{10}) & 2\,r_{1}\,r_{6}\,\sin({\theta_{1}}-{
2547
\theta_{6}})\,(m_{6}+2\,m_{9}+2\,m_{10}+2\,m_{7}+2\,m_{8}) & 2\,r_{1}
2548
\,r_{7}\,\sin({\theta_{1}}-{\theta_{7}})\,(2\,m_{10}+m_{7}+2\,m_{8}+2
2549
\,m_{9}) & 2\,r_{1}\,r_{8}\,\sin({\theta_{1}}-{\theta_{8}})\,(m_{8}+2
2550
\,m_{10}+2\,m_{9}) & 2\,r_{1}\,r_{9}\,\sin({\theta_{1}}-{\theta_{9}})
2551
\,(m_{9}+2\,m_{10}) & 2\,r_{1}\,m_{10}\,r_{10}\,\sin({\theta_{1}}-{
2552
\theta_{10}}) \cr -2\,r_{1}\,r_{2}\,\sin({\theta_{1}}-{\theta_{2}})\,(
2553
2\,m_{3}+m_{2}+2\,m_{4}+2\,m_{7}+2\,m_{10}+2\,m_{5}+2\,m_{6}+2\,m_{9}+
2554
2\,m_{8}) & 0 & 2\,r_{2}\,r_{3}\,\sin({\theta_{2}}-{\theta_{3}})\,(2\,
2555
m_{5}+2\,m_{4}+2\,m_{10}+2\,m_{8}+2\,m_{7}+m_{3}+2\,m_{9}+2\,m_{6}) &
2556
2\,r_{2}\,r_{4}\,\sin({\theta_{2}}-{\theta_{4}})\,(2\,m_{8}+m_{4}+2\,m
2557
_{9}+2\,m_{5}+2\,m_{7}+2\,m_{10}+2\,m_{6}) & 2\,r_{2}\,r_{5}\,\sin({
2558
\theta_{2}}-{\theta_{5}})\,(2\,m_{6}+2\,m_{8}+2\,m_{9}+2\,m_{7}+m_{5}+
2559
2\,m_{10}) & 2\,r_{2}\,r_{6}\,\sin({\theta_{2}}-{\theta_{6}})\,(m_{6}+
2560
2\,m_{9}+2\,m_{10}+2\,m_{7}+2\,m_{8}) & 2\,r_{2}\,r_{7}\,\sin({\theta
2561
_{2}}-{\theta_{7}})\,(2\,m_{10}+m_{7}+2\,m_{8}+2\,m_{9}) & 2\,r_{2}\,r
2562
_{8}\,\sin({\theta_{2}}-{\theta_{8}})\,(m_{8}+2\,m_{10}+2\,m_{9}) & 2
2563
\,r_{2}\,r_{9}\,\sin({\theta_{2}}-{\theta_{9}})\,(m_{9}+2\,m_{10}) & 2
2564
\,r_{2}\,m_{10}\,r_{10}\,\sin({\theta_{2}}-{\theta_{10}}) \cr -2\,r_{1
2565
}\,r_{3}\,\sin({\theta_{1}}-{\theta_{3}})\,(2\,m_{5}+2\,m_{4}+2\,m_{10
2566
}+2\,m_{8}+2\,m_{7}+m_{3}+2\,m_{9}+2\,m_{6}) & -2\,r_{2}\,r_{3}\,\sin(
2567
{\theta_{2}}-{\theta_{3}})\,(2\,m_{5}+2\,m_{4}+2\,m_{10}+2\,m_{8}+2\,m
2568
_{7}+m_{3}+2\,m_{9}+2\,m_{6}) & 0 & 2\,r_{3}\,r_{4}\,\sin({\theta_{3}}
2569
-{\theta_{4}})\,(2\,m_{8}+m_{4}+2\,m_{9}+2\,m_{5}+2\,m_{7}+2\,m_{10}+2
2570
\,m_{6}) & 2\,r_{3}\,r_{5}\,\sin({\theta_{3}}-{\theta_{5}})\,(2\,m_{6}
2571
+2\,m_{8}+2\,m_{9}+2\,m_{7}+m_{5}+2\,m_{10}) & 2\,r_{3}\,r_{6}\,\sin({
2572
\theta_{3}}-{\theta_{6}})\,(m_{6}+2\,m_{9}+2\,m_{10}+2\,m_{7}+2\,m_{8}
2573
) & 2\,r_{3}\,r_{7}\,\sin({\theta_{3}}-{\theta_{7}})\,(2\,m_{10}+m_{7}
2574
+2\,m_{8}+2\,m_{9}) & 2\,r_{3}\,r_{8}\,\sin({\theta_{3}}-{\theta_{8}})
2575
\,(m_{8}+2\,m_{10}+2\,m_{9}) & 2\,r_{3}\,r_{9}\,\sin({\theta_{3}}-{
2576
\theta_{9}})\,(m_{9}+2\,m_{10}) & 2\,r_{3}\,m_{10}\,r_{10}\,\sin({
2577
\theta_{3}}-{\theta_{10}}) \cr -2\,r_{1}\,r_{4}\,\sin({\theta_{1}}-{
2578
\theta_{4}})\,(2\,m_{8}+m_{4}+2\,m_{9}+2\,m_{5}+2\,m_{7}+2\,m_{10}+2\,
2579
m_{6}) & -2\,r_{2}\,r_{4}\,\sin({\theta_{2}}-{\theta_{4}})\,(2\,m_{8}+
2580
m_{4}+2\,m_{9}+2\,m_{5}+2\,m_{7}+2\,m_{10}+2\,m_{6}) & -2\,r_{3}\,r_{4
2581
}\,\sin({\theta_{3}}-{\theta_{4}})\,(2\,m_{8}+m_{4}+2\,m_{9}+2\,m_{5}+
2582
2\,m_{7}+2\,m_{10}+2\,m_{6}) & 0 & 2\,r_{4}\,r_{5}\,\sin({\theta_{4}}-
2583
{\theta_{5}})\,(2\,m_{6}+2\,m_{8}+2\,m_{9}+2\,m_{7}+m_{5}+2\,m_{10})
2584
& 2\,r_{4}\,r_{6}\,\sin({\theta_{4}}-{\theta_{6}})\,(m_{6}+2\,m_{9}+2
2585
\,m_{10}+2\,m_{7}+2\,m_{8}) & 2\,r_{4}\,r_{7}\,\sin({\theta_{4}}-{
2586
\theta_{7}})\,(2\,m_{10}+m_{7}+2\,m_{8}+2\,m_{9}) & 2\,r_{4}\,r_{8}\,
2587
\sin({\theta_{4}}-{\theta_{8}})\,(m_{8}+2\,m_{10}+2\,m_{9}) & 2\,r_{4}
2588
\,r_{9}\,\sin({\theta_{4}}-{\theta_{9}})\,(m_{9}+2\,m_{10}) & 2\,r_{4}
2589
\,m_{10}\,r_{10}\,\sin({\theta_{4}}-{\theta_{10}}) \cr -2\,r_{1}\,r_{5
2590
}\,\sin({\theta_{1}}-{\theta_{5}})\,(2\,m_{6}+2\,m_{8}+2\,m_{9}+2\,m_{
2591
7}+m_{5}+2\,m_{10}) & -2\,r_{2}\,r_{5}\,\sin({\theta_{2}}-{\theta_{5}}
2592
)\,(2\,m_{6}+2\,m_{8}+2\,m_{9}+2\,m_{7}+m_{5}+2\,m_{10}) & -2\,r_{3}\,
2593
r_{5}\,\sin({\theta_{3}}-{\theta_{5}})\,(2\,m_{6}+2\,m_{8}+2\,m_{9}+2
2594
\,m_{7}+m_{5}+2\,m_{10}) & -2\,r_{4}\,r_{5}\,\sin({\theta_{4}}-{\theta
2595
_{5}})\,(2\,m_{6}+2\,m_{8}+2\,m_{9}+2\,m_{7}+m_{5}+2\,m_{10}) & 0 & 2
2596
\,r_{5}\,r_{6}\,\sin({\theta_{5}}-{\theta_{6}})\,(m_{6}+2\,m_{9}+2\,m
2597
_{10}+2\,m_{7}+2\,m_{8}) & 2\,r_{5}\,r_{7}\,\sin({\theta_{5}}-{\theta
2598
_{7}})\,(2\,m_{10}+m_{7}+2\,m_{8}+2\,m_{9}) & 2\,r_{5}\,r_{8}\,\sin({
2599
\theta_{5}}-{\theta_{8}})\,(m_{8}+2\,m_{10}+2\,m_{9}) & 2\,r_{5}\,r_{9
2600
}\,\sin({\theta_{5}}-{\theta_{9}})\,(m_{9}+2\,m_{10}) & 2\,r_{5}\,m_{
2601
10}\,r_{10}\,\sin({\theta_{5}}-{\theta_{10}}) \cr -2\,r_{1}\,r_{6}\,
2602
\sin({\theta_{1}}-{\theta_{6}})\,(m_{6}+2\,m_{9}+2\,m_{10}+2\,m_{7}+2
2603
\,m_{8}) & -2\,r_{2}\,r_{6}\,\sin({\theta_{2}}-{\theta_{6}})\,(m_{6}+2
2604
\,m_{9}+2\,m_{10}+2\,m_{7}+2\,m_{8}) & -2\,r_{3}\,r_{6}\,\sin({\theta
2605
_{3}}-{\theta_{6}})\,(m_{6}+2\,m_{9}+2\,m_{10}+2\,m_{7}+2\,m_{8}) & -2
2606
\,r_{4}\,r_{6}\,\sin({\theta_{4}}-{\theta_{6}})\,(m_{6}+2\,m_{9}+2\,m
2607
_{10}+2\,m_{7}+2\,m_{8}) & -2\,r_{5}\,r_{6}\,\sin({\theta_{5}}-{\theta
2608
_{6}})\,(m_{6}+2\,m_{9}+2\,m_{10}+2\,m_{7}+2\,m_{8}) & 0 & 2\,r_{6}\,r
2609
_{7}\,\sin({\theta_{6}}-{\theta_{7}})\,(2\,m_{10}+m_{7}+2\,m_{8}+2\,m
2610
_{9}) & 2\,r_{6}\,r_{8}\,\sin({\theta_{6}}-{\theta_{8}})\,(m_{8}+2\,m
2611
_{10}+2\,m_{9}) & 2\,r_{6}\,r_{9}\,\sin({\theta_{6}}-{\theta_{9}})\,(m
2612
_{9}+2\,m_{10}) & 2\,r_{6}\,m_{10}\,r_{10}\,\sin({\theta_{6}}-{\theta
2613
_{10}}) \cr -2\,r_{1}\,r_{7}\,\sin({\theta_{1}}-{\theta_{7}})\,(2\,m_{
2614
10}+m_{7}+2\,m_{8}+2\,m_{9}) & -2\,r_{2}\,r_{7}\,\sin({\theta_{2}}-{
2615
\theta_{7}})\,(2\,m_{10}+m_{7}+2\,m_{8}+2\,m_{9}) & -2\,r_{3}\,r_{7}\,
2616
\sin({\theta_{3}}-{\theta_{7}})\,(2\,m_{10}+m_{7}+2\,m_{8}+2\,m_{9})
2617
& -2\,r_{4}\,r_{7}\,\sin({\theta_{4}}-{\theta_{7}})\,(2\,m_{10}+m_{7}
2618
+2\,m_{8}+2\,m_{9}) & -2\,r_{5}\,r_{7}\,\sin({\theta_{5}}-{\theta_{7}}
2619
)\,(2\,m_{10}+m_{7}+2\,m_{8}+2\,m_{9}) & -2\,r_{6}\,r_{7}\,\sin({
2620
\theta_{6}}-{\theta_{7}})\,(2\,m_{10}+m_{7}+2\,m_{8}+2\,m_{9}) & 0 & 2
2621
\,r_{7}\,r_{8}\,\sin({\theta_{7}}-{\theta_{8}})\,(m_{8}+2\,m_{10}+2\,m
2622
_{9}) & 2\,r_{7}\,r_{9}\,\sin({\theta_{7}}-{\theta_{9}})\,(m_{9}+2\,m
2623
_{10}) & 2\,r_{7}\,m_{10}\,r_{10}\,\sin({\theta_{7}}-{\theta_{10}})
2624
\cr -2\,r_{1}\,r_{8}\,\sin({\theta_{1}}-{\theta_{8}})\,(m_{8}+2\,m_{
2625
10}+2\,m_{9}) & -2\,r_{2}\,r_{8}\,\sin({\theta_{2}}-{\theta_{8}})\,(m
2626
_{8}+2\,m_{10}+2\,m_{9}) & -2\,r_{3}\,r_{8}\,\sin({\theta_{3}}-{\theta
2627
_{8}})\,(m_{8}+2\,m_{10}+2\,m_{9}) & -2\,r_{4}\,r_{8}\,\sin({\theta_{4
2628
}}-{\theta_{8}})\,(m_{8}+2\,m_{10}+2\,m_{9}) & -2\,r_{5}\,r_{8}\,\sin(
2629
{\theta_{5}}-{\theta_{8}})\,(m_{8}+2\,m_{10}+2\,m_{9}) & -2\,r_{6}\,r
2630
_{8}\,\sin({\theta_{6}}-{\theta_{8}})\,(m_{8}+2\,m_{10}+2\,m_{9}) & -2
2631
\,r_{7}\,r_{8}\,\sin({\theta_{7}}-{\theta_{8}})\,(m_{8}+2\,m_{10}+2\,m
2632
_{9}) & 0 & 2\,r_{8}\,r_{9}\,\sin({\theta_{8}}-{\theta_{9}})\,(m_{9}+2
2633
\,m_{10}) & 2\,r_{8}\,m_{10}\,r_{10}\,\sin({\theta_{8}}-{\theta_{10}})
2634
\cr -2\,r_{1}\,r_{9}\,\sin({\theta_{1}}-{\theta_{9}})\,(m_{9}+2\,m_{
2635
10}) & -2\,r_{2}\,r_{9}\,\sin({\theta_{2}}-{\theta_{9}})\,(m_{9}+2\,m
2636
_{10}) & -2\,r_{3}\,r_{9}\,\sin({\theta_{3}}-{\theta_{9}})\,(m_{9}+2\,
2637
m_{10}) & -2\,r_{4}\,r_{9}\,\sin({\theta_{4}}-{\theta_{9}})\,(m_{9}+2
2638
\,m_{10}) & -2\,r_{5}\,r_{9}\,\sin({\theta_{5}}-{\theta_{9}})\,(m_{9}+
2639
2\,m_{10}) & -2\,r_{6}\,r_{9}\,\sin({\theta_{6}}-{\theta_{9}})\,(m_{9}
2640
+2\,m_{10}) & -2\,r_{7}\,r_{9}\,\sin({\theta_{7}}-{\theta_{9}})\,(m_{9
2641
}+2\,m_{10}) & -2\,r_{8}\,r_{9}\,\sin({\theta_{8}}-{\theta_{9}})\,(m_{
2642
9}+2\,m_{10}) & 0 & 2\,r_{9}\,m_{10}\,r_{10}\,\sin({\theta_{9}}-{
2643
\theta_{10}}) \cr -2\,r_{1}\,m_{10}\,r_{10}\,\sin({\theta_{1}}-{\theta
2644
_{10}}) & -2\,r_{2}\,m_{10}\,r_{10}\,\sin({\theta_{2}}-{\theta_{10}})
2645
& -2\,r_{3}\,m_{10}\,r_{10}\,\sin({\theta_{3}}-{\theta_{10}}) & -2\,r
2646
_{4}\,m_{10}\,r_{10}\,\sin({\theta_{4}}-{\theta_{10}}) & -2\,r_{5}\,m
2647
_{10}\,r_{10}\,\sin({\theta_{5}}-{\theta_{10}}) & -2\,r_{6}\,m_{10}\,r
2648
_{10}\,\sin({\theta_{6}}-{\theta_{10}}) & -2\,r_{7}\,m_{10}\,r_{10}\,
2649
\sin({\theta_{7}}-{\theta_{10}}) & -2\,r_{8}\,m_{10}\,r_{10}\,\sin({
2650
\theta_{8}}-{\theta_{10}}) & -2\,r_{9}\,m_{10}\,r_{10}\,\sin({\theta_{
2651
9}}-{\theta_{10}}) & 0 \end{array} \right) $$
2654
$$ \left( \begin{array}{c} g\,r_{1}\,\cos({\theta_{1}})\,(m_{1}+2\,m_{
2655
9}+2\,m_{2}+2\,m_{4}+2\,m_{3}+2\,m_{8}+2\,m_{7}+2\,m_{6}+2\,m_{5}+2\,m
2656
_{10}) \cr g\,r_{2}\,\cos({\theta_{2}})\,(2\,m_{3}+m_{2}+2\,m_{4}+2\,m
2657
_{7}+2\,m_{10}+2\,m_{5}+2\,m_{6}+2\,m_{9}+2\,m_{8}) \cr g\,r_{3}\,\cos
2658
({\theta_{3}})\,(2\,m_{5}+2\,m_{4}+2\,m_{10}+2\,m_{8}+2\,m_{7}+m_{3}+2
2659
\,m_{9}+2\,m_{6}) \cr g\,r_{4}\,\cos({\theta_{4}})\,(2\,m_{8}+m_{4}+2
2660
\,m_{9}+2\,m_{5}+2\,m_{7}+2\,m_{10}+2\,m_{6}) \cr g\,r_{5}\,\cos({
2661
\theta_{5}})\,(2\,m_{6}+2\,m_{8}+2\,m_{9}+2\,m_{7}+m_{5}+2\,m_{10})
2662
\cr g\,r_{6}\,\cos({\theta_{6}})\,(m_{6}+2\,m_{9}+2\,m_{10}+2\,m_{7}+
2663
2\,m_{8}) \cr g\,r_{7}\,\cos({\theta_{7}})\,(2\,m_{10}+m_{7}+2\,m_{8}+
2664
2\,m_{9}) \cr g\,\cos({\theta_{8}})\,r_{8}\,(m_{8}+2\,m_{10}+2\,m_{9})
2665
\cr g\,r_{9}\,\cos({\theta_{9}})\,(m_{9}+2\,m_{10}) \cr m_{10}\,g\,r
2666
_{10}\,\cos({\theta_{10}}) \end{array} \right) $$
2667
Since $M,C,R$ only depends on $\theta$
2668
,we can forget $x_i,y_i$ in the dynamical system
2669
and just keep the $\dot{theta}=\eta$ in the constraints
added
removed
demos/npend/Maple/systeme.tex
