约束Hamilton系统Mei对称性的摄动和绝热不变量

Perturbation and adiabatic invariants of Mei symmetry for constrained Hamilton system

基于一般力学系统的对称性与守恒量理论,研究了相空间中奇异系统Mei对称性的摄动与绝热不变量问题.首先,给出了约束Hamilton系统的正则方程、系统Mei对称性确定方程、限制方程、附加限制方程以及结构方程和精确不变量的存在形式,在此基础上研究了系统正则方程受微扰后,系统无限小生成元的变化,得到了系统Mei对称性摄动确定方程以及导致的Mei绝热不变量的形式和条件;其次,讨论了系统Mei对称性摄动与Noether对称性摄动、Lie对称性摄动之间的关系,并寻求了其他形式的高阶绝热不变量;最后,通过实例验证了本文结果的正确性.

Based on the theory of symmetry and conservation in general mechanical systems,the perturbation and adiabatic invariants of Mei symmetry of singular system in phase space are studied.Firstly,we give the canonical equations of the constrained Hamilton system,the determining equations of Mei symmetry,the restricted equations and the additional constraint equations,as well as the structural equations and the form of exact invariant,meanwhile,we study the change of the infinitesimal generating elements when the canonical equations are perturbed,and we get the perturbation determining equations of Mei symmetry,the condition and the form of Mei type adiabatic invariants.Secondly,we discuss the relationship among the perturbation of Mei symmetry,Noether symmetry and Lie symmetry,and seek other forms of high-order adiabatic invariants.Finally,the correctness of the results of this paper are verified by an example.