双连杆机械臂的差分离散和Noether对称性

Noether symmetry and difference discretization of double-link manipulator

通过连续的变分原理,给出双连杆机械臂的Euler-Lagrange方程。将差分看成一个整体的几何对象,对连续的平面双连杆机械臂的模型进行保结构离散,得到双连杆机械臂的差分动力学方程的具体形式。通过离散的Noether定理,给出双连杆机械臂的Noether对称性判定方程和离散守恒量的具体形式。

the Euler-Lagrange equations of double-link manipulator are proposed via the variational principle. Structure preserving discretization is applied to the equations of the system. The difference equations of the systems are obtained by means of difference discrete variational principle with the difference being regarded as an entire geometric object. The forms of Noether identity and conserved quantity of the double-link manipulator are constructed via the difference Noether theorem.