变质量单面完整约束系统Lie对称性的摄动与广义Hojman型绝热不变量

研究变质量单面完整约束系统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. 关键词： 变质量 单面完整约束 对称性 摄动 绝热不变量

Perturbation of Lie symmetries and a type of generalized Hojman adiabatic invariants for variable mass systems with unilateral holonomic constraints

In this paper, the perturbation problem of Lie symmetries and adiabatic invariants for variable mass systems with unilateral holonomic constraints are studied. Firstly, a type of generalized Hojman conserved quantity under general infinitesimal transformation is obtained. Then, based on the definition of high-order adiabatic invariants of a mechanical system, the perburbation of Lie symmetries for variable mass systems with unilateral holonomic constraints under small disturbance is discussed and a type of generalized Hojman adiabatic invariants are given. At last, an example to illustrate the application of the results is given.