Lie symmetrical perturbation and adiabatic invariants of generalized Hojman type for Lagrange systems |
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| Authors: | Luo Shao-Kai Chen Xiang-Wei and Guo Yong-Xin |
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| Affiliation: | Institute of Mathematical Mechanics and Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China; Key Laboratory of Advanced Textile Materials and Manufacturing Technology (Zhejiang Sci-Tech University), Ministry of Education, Hangzhou 310018, China; Department of Physics, Shangqiu Teachers College, Shangqiu 476000, China; Department of Physics, Liaoning University, Shenyang 110036, China |
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| 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. |
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| Keywords: | Lagrange system Lie symmetrical
perturbation exact invariant adiabatic invariant of generalized
Hojman type |
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