質量行列
M = diag  [ m 1 I n 1 , m 2 I n 2 , ... , m N I n N ] {\displaystyle M=\operatorname {diag} \left[m_{1}I_{n_{1}},\,m_{2}I_{n_{2}},\,\ldots ,\,m_{N}I_{n_{N}}\right]}
niが'I×N I nは単位行列、または:
q = [ x y α ] {\displaystyle q={\begin{bmatrix}x&y&\alpha \end{bmatrix}}}
x 1 = ( x , y ) + R ( cos  α , sin  α ) v 1 = ( x ̇ , y ̇ ) + R α ̇ ( − sin  α , cos  α ) x 2 = ( x , y ) − R ( cos  α , sin  α ) v 2 = ( x ̇ , y ̇ ) − R α ̇ ( − sin  α , cos  α ) {\displaystyle {\begin{aligned}x_{1}&=(x,y)+R(\cos \alpha ,\sin \alpha )&v_{1}&=\left({\dot {x}},{\dot {y}}\right)+R{\dot {\alpha }}(-\sin \alpha ,\cos \alpha )\\x_{2}&=(x,y)-R(\cos \alpha ,\sin \alpha )&v_{2}&=\left({\dot {x}},{\dot {y}}\right)-R{\dot {\alpha }}(-\sin \alpha ,\cos \alpha )\end{aligned}}}