准坐标下广义力学系统的Lie对称定理及其逆定理

LIE SYMMETRIES THEOREM AND ITS INVERSE OF GENERALIZED MECHANICAL SYSTEMS IN TERMS OF QUASI-COORDINATES

研究准坐标下广义力学系统的Lie对称性与守恒量 .首先 ,对准坐标下广义力学系统定义无限小生成元 ,并应用微分方程在无限小变换下不变性的Lie方法 ,建立系统的确定方程 .其次 ,给出结构方程和守恒量的形式 .最后 ,研究Lie对称性逆问题 (由已知积分求Lie对称 )并举例说明结果的应用 .

In this paper, Lie symmetries and conserved quantities of generalized mechanical systems in terms of quasi-coordinates were studied. First, the definition of an infinitesimal generator for the generalized mechanical systems in terms of quasi-coordinates were given, then the determining equations of the Lie symmetries were established by using Lie's method of invariance of ordinary differential equations under infinitesimal transformations. Next, the structure equation and the form of conserved quantities were obtained. Finally, the inverse problem of Lie symmetries systems were discussed and an example to illustrate the application of the result was given.