广义经典力学中Poincaré-Chetaev方程的Lie对称性与守恒量

Lie Symmetries and Conserved Quantities of Poincaré-Chetaev Equations In Generalized Classical Mechanics

本文建立广义经典力学中的PoincaréChetaev方程。利用常微分方程在无限小变换下的不变性研究它的Lie对称性,得到确定方程,限制附加方程,结构方程和守恒量的形成,并举例说明结果的应用。

The PoincaréChetaev equations in generalized classical mechanics were established,and the invariance of the ordinary differential equations under the infinitesimal transformations was used to study the symmetries of the equations.The determining equations,the supplement restriction equations,the structure equations and the form of conserved quantities were obtained.An example was given to illustrate the application of the result.