%0 Journal Article
%T Lie symmetrical perturbation and adiabatic invariants of generalized Hojman type for Lagrange systems
%A Luo Shao-Kai
%A Chen Xiang-Wei
%A Guo Yong-Xin
%A <br>罗绍凯
%A 陈向炜
%A 郭永新
%J 中国物理 B
%D 2007
%I 
%X 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.
%K Lagrange system
%K Lie symmetrical perturbation
%K exact invariant
%K adiabatic invariant of generalized Hojman type<br>拉格朗日系统
%K Lie对称干扰
%K 精确不变量
%K 微分方程
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=47EA7CFDDEBB28E0&jid=CD8D6A6897B9334F09D8D1648C376FB4&aid=51EC29F0F1FE4796BD05D5BA99D95233&yid=A732AF04DDA03BB3&vid=7801E6FC5AE9020C&iid=708DD6B15D2464E8&sid=389B0D33D859BE05&eid=0A97B65BD82A9CE2&journal_id=1009-1963&journal_name=中国物理&referenced_num=0&reference_num=0