机电系统Lie对称性的摄动和广义Hojman型绝热不变量

摘要

研究机电系统Lie对称性的摄动与广义Hojman型绝热不变量.首先通过一般无限小变换下的Lie对称性得到广义Hojman型的守恒量;然后基于力学系统高阶绝热不变量的定义,研究小扰动作用下系统Lie对称性的摄动,得到系统广义Hojman型绝热不变量.最后举例说明结果的应用.%The perturbation problem of Lie symmetries and adiabatic invariants for mechanico-electrical systems are studied.Firstly,a type of generalized Hojman's conserved quantity under general infinitesimal transformation is obtained.Then,based on the definition of high-order adiabatic invariants of a mechanical system,the perturbation of Lie symmetries for mechanico-electrical systems under small disturbance is discussed and a type of generalized. Hojman's adiabatic invariants are given.At last,an example to illustrate the application of the results is given.