广义Birkhoff系统的分离变量与局部能量积分

Separation of variables and integrals of partial energy for a generalized Birkhoffian system

为了进一步研究约束力学系统的第一积分与动力学性质,提出并研究广义Birkhoff系统的分离变量与局部能量积分。从广义Birkhoff方程出发,分别研究了分离变量为单变量和耦合变量时,广义Birkhoff系统存在局部能量积分的条件及其形式,并将结果应用于Birkhoff系统。文末举例说明结果的应用。

In order to further study the first integral and corresponding dynamical property for a constrained mechanical system袁this paper proposed and explored the separation of variables and the integrals of partial energy for a generalized Birkhoffian system.Out of the generalized Birkhoff equation袁the conditions and the forms of the integrals of partial energy in the generalized Birkhoffian system are investigated when the separated variables are single and coupled respectively.The results are applied to the Birkhoffian system.Finally袁four examples are given to illustrate the application of the results.