基于非标准Lagrange函数的动力学系统的Routh降阶法

Routh Method of Reduction for Dynamic Systems with Non-Standard Lagrangians

研究基于指数Lagrange函数与Lagrange函数幂函数两种非标准Lagrange函数的动力学系统的循环积分与Routh降阶法.首先,给出了循环坐标的定义,并利用循环坐标与基于非标准Lagrange函数的系统的Lagrange方程,得到了循环积分的形式;其次,将Routh降阶法加以推广,建立了基于非标准Lagrange函数的动力学系统的Routh方程,并举例说明结果的应用.

The cyclic integral and Routh method of reduction for the dynamic system based on exponential Lagrangians and power law Lagrangians were studied. Firstly, the cyclic coordinate was defined, and the form of cyclic integral were obtained by using cyclic coordinates and Lagrange equations of the system with non-standard Lagrangians. Then, the Routh method of reduction was extended, the Routh equations for the dynamic system with non-standard Lagrangians were established. Two examples were given to illustrate the application of the results.