准坐标下Poincaré-Chetaev方程的Lie对称性与守恒量  

Lie symmetries and conserved quantities of Poincare-Chetaev equations in terms quasi-coordinates

作　　者：赵淑红[1] 

机构地区：[1]东北农业大学工程学院,黑龙江哈尔滨150030

出　　处：《商丘师范学院学报》2002年第2期3-7,共5页Journal of Shangqiu Normal University

基　　金：黑龙江自然科学基金资助项目(199507)

摘　　要：建立准坐标下完整力学系统的Poincare-Chetaev方程.给出准坐标下系统的无限小生成元的定义,利用常微分方程在无限小变换下的不变性质研究它的Lie对称性,得到确定方程、结构方程和守恒量的形式.并举例说明结果的应用.In this paper, Lie symmetries and conserved quantities of Poincare-chetaev equations in terms of quasi-coordinates were studied. Firsty, the Poincare-chetaev equations of holonomic mechanical systems in terms of quasi-coordinates were established, and the definition of an infinitesimal generator for the mechanical systems in terms of quasi-coordinates was given. Secondly, the invariance of the ordinary differential equations under the infinitesimal transformations was used to study the Lie symmetries of the equations, then determining equations and the structure equations and the form of conserved quantities were obtained. Finally, an example was given to illustrate the application of the result.

关 键 词：准坐标 POINCARÉ-CHETAEV方程 LIE对称性 守恒量 

分 类 号：O316[理学—一般力学与力学基础]