Lie symmetrical perturbation and adiabatic invariants of generalized Hojman type for Lagrange systems
Luo Shao-Kai(罗绍凯)a)b)†, Chen Xiang-Wei(陈向炜)c), and Guo Yong-Xin(郭永新)d)
a Institute of Mathematical Mechanics and Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China; b Key Laboratory of Advanced Textile Materials and Manufacturing Technology (Zhejiang Sci-Tech University), Ministry of Education, Hangzhou 310018, China; c Department of Physics, Shangqiu Teachers College, Shangqiu 476000, China; d Department of Physics, Liaoning University, Shenyang 110036, China
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.
Fund: Project supported by the National
Natural Science Foundation of China (Grant Nos 10472040 and
10372053), the Natural Science Foundation of Hunan Province, China
(Grant No 03JJY3005), the Natural Science Foundation of Henan
Province, China (Grant No 031101
Cite this article:
Luo Shao-Kai(罗绍凯), Chen Xiang-Wei(陈向炜), and Guo Yong-Xin(郭永新) Lie symmetrical perturbation and adiabatic invariants of generalized Hojman type for Lagrange systems 2007 Chinese Physics 16 3176
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