中国物理B ›› 2005, Vol. 14 ›› Issue (3): 449-451.doi: 10.1088/1009-1963/14/3/001

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Form invariances and Lutzky conserved quantities for Lagrange systems

梅凤翔1, 许学军2   

  1. (1)Department of Mechanics, Beijing Institute of Technology, Beijing 100081, China; (2)Department of Mechanics, Beijing Institute of Technology, Beijing 100081, China; Department of Physics, Zhejiang Normal University, Jinhua 321004, China
  • 收稿日期:2004-09-13 修回日期:2004-10-12 出版日期:2005-03-02 发布日期:2005-03-02
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10272021).

Form invariances and Lutzky conserved quantities for Lagrange systems

Mei Feng-Xiang (梅凤翔)a, Xu Xue-Jun (许学军)ab   

  1. a Department of Mechanics, Beijing Institute of Technology, Beijing 100081, China; b Department of Physics, Zhejiang Normal University, Jinhua 321004, China
  • Received:2004-09-13 Revised:2004-10-12 Online:2005-03-02 Published:2005-03-02
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10272021).

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摘要： This paper focuses on studying a form invariance which can result in a Lutzky conserved quantity for a Lagrange system. The criterion of the form invariance for the system is given. The necessary and sufficient condition under which the form invariance is a Lie symmetry for the system is obtained. Lutzky's result is utilized to prove that the form invariance can lead to a Lutzky conserved quantity. Two examples are finally given to illustrate the application of the result.

关键词: symmetry, form invariance, conserved quantity, Lagrange system

Abstract: This paper focuses on studying a form invariance which can result in a Lutzky conserved quantity for a Lagrange system. The criterion of the form invariance for the system is given. The necessary and sufficient condition under which the form invariance is a Lie symmetry for the system is obtained. Lutzky's result is utilized to prove that the form invariance can lead to a Lutzky conserved quantity. Two examples are finally given to illustrate the application of the result.

Key words: symmetry, form invariance, conserved quantity, Lagrange system

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

  • 45.05.+x
02.20.Qs (General properties, structure, and representation of Lie groups) 45.20.Jj (Lagrangian and Hamiltonian mechanics)