广义经典力学系统动力学方程积分的Jacobi最终乘子法

研究动力学系统的积分问题,将Jacobi最终乘子法应用于积分广义经典力学系统的动力学方程。建立了广义经典力学系统的运动微分方程;定义了广义经典力学系统的Jacobi最终乘子;研究了系统的第一积分与Jacobi最终乘子的关系。研究表明:对于位形由n个广义坐标确定且拉格朗日函数含有广义坐标对时间的ω阶导数的广义经典力学系统,如果已知系统的(2ωn-1)个第一积分,则可利用Jacobi最终乘子给出系统的解。文末举例说明结果的应用。

Method of Jacobi Last Multiplier for Solving Dynamics Equations Integration of Generalized Classical Mechanics System

The integration issues of dynamic system is studied,and the method of Jacobi last multiplier is applied to integrate dynamic equations of generalized classical mechanics systems.The differential equations of motion of a generalized classical mechanics system are given.The Jacobi last multiplier of the system is defined,and the relation between the Jacobi last multiplier and the first integrals of the system is discussed.The research shows that for a generalized classical mechanics system,whose configuration is determined by n generalized coordinates and Lagrangian contains ω-order derivatives of generalized coordinates with respect to time,the solution of the system can be found by the Jacobi last multiplier if(2ωn-1) first integrals of the system are known.Finally, an example is given to illustrate the application of the results.