中国物理B ›› 2008, Vol. 17 ›› Issue (10): 3542-3548.doi: 10.1088/1674-1056/17/10/003

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Adiabatic invariants of generalized Lutzky type for disturbed holonomic nonconservative systems

蔡建乐1, 罗绍凯2, 贾利群3   

  1. (1)Department of Physics, Hangzhou Teachers College, Hangzhou 310018, China; (2)Institute of Mathematical Mechanics and Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou { rm 310018, China; (3)School of Science，Southern Yangtze University, Wuxi 214122, China
  • 收稿日期:2008-01-10 修回日期:2008-01-21 出版日期:2008-10-20 发布日期:2008-10-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10372053).

Adiabatic invariants of generalized Lutzky type for disturbed holonomic nonconservative systems

Luo Shao-Kai(罗绍凯)a)†, Cai Jian-Le(蔡建乐)b), and Jia Li-Qun(贾利群)c)   

  1. a  Institute of Mathematical Mechanics and Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China; b Department of Physics, Hangzhou Teachers College, Hangzhou 310018, China; c School of Science，Southern Yangtze University, Wuxi 214122, China
  • Received:2008-01-10 Revised:2008-01-21 Online:2008-10-20 Published:2008-10-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10372053).

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摘要： Based on the definition of higher-order adiabatic invariants of a mechanical system, a new type of adiabatic invariants，i.e. generalized Lutzky adiabatic invariants, of a disturbed holonomic nonconservative mechanical system are obtained by investigating the perturbation of Lie symmetries for a holonomic nonconservative mechanical system with the action of small disturbance. The adiabatic invariants and the exact invariants of the Lutzky type of some special cases, for example, the Lie point symmetrical transformations, the special Lie symmetrical transformations, and the Lagrange system, are given. And an example is given to illustrate the application of the method and results.

关键词: analytical mechanics, disturbed holonomic nonconservative system, Lie symmetrical perturbation, adiabatic invariant of Lutzky type

Abstract: Based on the definition of higher-order adiabatic invariants of a mechanical system, a new type of adiabatic invariants，i.e. generalized Lutzky adiabatic invariants, of a disturbed holonomic nonconservative mechanical system are obtained by investigating the perturbation of Lie symmetries for a holonomic nonconservative mechanical system with the action of small disturbance. The adiabatic invariants and the exact invariants of the Lutzky type of some special cases, for example, the Lie point symmetrical transformations, the special Lie symmetrical transformations, and the Lagrange system, are given. And an example is given to illustrate the application of the method and results.

Key words: analytical mechanics, disturbed holonomic nonconservative system, Lie symmetrical perturbation, adiabatic invariant of Lutzky type

中图分类号:  (General theory of classical mechanics of discrete systems)

  • 45.05.+x
02.30.Jr (Partial differential equations)