积分二阶线性非完整力学系统的最终乘子方法

An integration method of a mechanical system with second order linear non-holonomic constraints

研究二阶线性非完整力学系统的积分方法。建立了相空间中二阶线性非完整力学系统的运动微分方程,给出了系统的Jacobi最终乘子的定义,研究了系统的第一积分与Jacobi最终乘子的关系。研究表明:由n个广义坐标确定的受有g个二阶非完整约束的力学系统,如果已知系统(2n-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。

A new integration method of a mechanical system with second order linear non-holonomic constraints is put forward. The differential equations of motion of the mechanical system with second order linear non-holo- nomic constraints in phase space are established. The Jacobi Last Multiplier of the system is defined and the re- lation between the Jacobi Last Multiplier and the first integrals of the system is discussed. The study shows that for a mechanical system with g second order linear non-holonomic constraints, whose configuration is determined by n generalized coordinates, the solution of the system can be found by the Jaeobi Last Multiplier if （2n-l） first integrals of the system are known. An example is given to illustrate the application of the results.