1. Lie symmetrical perturbation and adiabatic invariants of generalized Hojman type for Lagrange systems
- Author
-
Chen Xiang-Wei, Luo Shao-Kai, and Guo Yong-Xin
- Subjects
Physics ,Mechanical system ,Differential equation ,Infinitesimal ,Homogeneous space ,General Physics and Astronomy ,Perturbation (astronomy) ,Adiabatic process ,Mathematical physics - Abstract
Based on the invariance of differential equations under infinitesimal transformations of group, Lie symmetries, exact invariants, perturbation to the symmetries and adiabatic invariants in form of non-Noether for a Lagrange system are presented. Firstly, the exact invariants of generalized Hojman type led directly by Lie symmetries for a Lagrange system without perturbations are given. Then, on the basis of the concepts of Lie symmetries and higher order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for the system with the action of small disturbance is investigated, the adiabatic invariants of generalized Hojman type for the system are directly obtained, the conditions for existence of the adiabatic invariants and their forms are proved. Finally an example is presented to illustrate these results.
- Published
- 2007