广义经典力学系统对称性的摄动与绝热不变量

在高维增广相空间中研究广义经典力学系统的精确不变量和绝热不变量.建立了该空间中系 统的对称性与不变量的关系；基于力学系统受到小干扰力作用的高阶绝热不变量的概念，给出了系统的高阶绝热不变量的形式及存在条件，并建立了绝热不变量与对称变换之间的对应关系；最后，举例说明结果的应用. 关键词： 对称性 摄动 不变量 广义经典力学系统 增广相空间

Perturbation to symmetries and adiabatic invariant for systems of generalized c lassical mechanics

This paper studies the exact invariants and the adiabatic invariants for systems of generalized classical mechanics in the high-dimensional extended phase space and gives the relations between the invariants and the symmetries of the system s in the space. Based on the concept of high-order adiabatic invariant of mechan ical systems with the action of small disturbance, it presents the form of the h igh-order adiabatic invariant and the conditions for their existence,and establi shes the relationship between adiabatic invariant and symmetrical transformation . In the end of this paper, an example is given to illustrate the application of the results.