非保守力学系统的Lie对称性和守恒量

CONSERVATVE QUANTITIES AND LIE'S SYMMETRIES OF NONCONSERVATIVE DYNAMICAL SYSTEMS

本文讨论非保守力学系统的Ｌｉｅ对称性，给出由Ｌｉｅ对称性得到力学系统守恒量的条件，并给出了说明性的例子，在文章最后，还说明对于非保守系统，它的Ｎｏｅｔｈｅｒ对称性并不一定是其自身的Ｌｉｅ对称性。

This paper discusses Lie’s symmetry of nonconservative mechanical sys-tems. The existence conditions of conservative quantities corresponding with Lie's symmetryare est ablished. Two illustrative examples are given. Finally, we explain from an examplethat Noether's symmetry may not be Lie's symmetry for nonconservative mechanical system.