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A New Type of Non-Noether Adiabatic Invariants for Disturbed Lagrangian Systems: Adiabatic Invariants of Generalized Lutzky Type
引用本文:罗绍凯.A New Type of Non-Noether Adiabatic Invariants for Disturbed Lagrangian Systems: Adiabatic Invariants of Generalized Lutzky Type[J].中国物理快报,2007,24(9):2463-2466.
作者姓名:罗绍凯
作者单位:[1]Institute of Mathematical Mechanics and Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018 [2]Key Laboratory of Advanced Textile Materials and Manufacturing Technology (Ministry of Education), Zhejiang Sci-Tech University, Hangzhou 310018
基金项目:Sponsored by the National Natural Science Foundation of China under Grant Nos 10372053 and 10472040.
摘    要:For a Lagrangian system with the action of small disturbance, the Lie symmetrical perturbation and a new type of non-Noether adiabatic invariant are presented in general infinitesimal transformation groups. On the basis of the invariance of disturbed Lagrangian systems under general infinitesimal transformations, the determining equations of Lie symmetries of the system are constructed. Based on the definition of higher-order adiabatic invariants of a mechanical system, a new type of adiabatic invariant, i.e. generalized Lutzky adiabatic invariants, of a disturbed Lagrangian system are obtained by investigating the perturbation of Lie symmetries t'or a Lagrangian system with the action of small disturbance. Finally, an example is given to illustrate the application of the method and results.

关 键 词:绝热性能  拉格朗日算子  不变量  物理学
收稿时间:2007-6-6
修稿时间:2007-06-06

A New Type of Non-Noether Adiabatic Invariants for Disturbed Lagrangian Systems: Adiabatic Invariants of Generalized Lutzky Type
LUO Shao-Kai.A New Type of Non-Noether Adiabatic Invariants for Disturbed Lagrangian Systems: Adiabatic Invariants of Generalized Lutzky Type[J].Chinese Physics Letters,2007,24(9):2463-2466.
Authors:LUO Shao-Kai
Institution:1.Institute of Mathematical Mechanics and Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018 ;2. Key Laboratory of Advanced Textile Materials and Manufacturing Technology (Ministry of Education
Abstract:For a Lagrangian system with the action of small disturbance, the Lie symmetrical perturbation and a new type of non-Noether adiabatic invariant are presented in general infinitesimal transformation groups. On the basis of the invariance of disturbed Lagrangian systems under general infinitesimal transformations, the determining equations of Lie symmetries of the system are constructed. Based on the definition of higher-order adiabatic invariants of a mechanical system, a new type of adiabatic invariant, i.e. generalized Lutzky adiabatic invariants, of a disturbed Lagrangian system are obtained byinvestigating the perturbation of Lie symmetries for a Lagrangian system with the action of small disturbance. Finally, an example is given to illustrate the application of the method and results.
Keywords:02  20  Sv
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