中国物理B ›› 2004, Vol. 13 ›› Issue (12): 1999-2002.doi: 10.1088/1009-1963/13/12/004

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Non-Noether conserved quantity constructed by using form invariance for Birkhoffian system

梅凤翔1, 秦茂昌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:2004-05-11 修回日期:2004-06-03 出版日期:2004-12-17 发布日期:2005-03-17
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10272021).

Non-Noether conserved quantity constructed by using form invariance for Birkhoffian system

Xu Xue-Jun (许学军)ab, Mei Feng-Xiang (梅凤翔)a, Qin Mao-Chang (秦茂昌)a   

  1. a Department of Mechanics, Beijing Institute of Technology, Beijing 100081, China; b Department of Physics, Zhejiang Normal University, Jinhua 321004, China
  • Received:2004-05-11 Revised:2004-06-03 Online:2004-12-17 Published:2005-03-17
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10272021).

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摘要： Based on the invariance of Birkhoffian equations under the infinitesimal transformations of groups, the definition and the criterion of a form invariance for a Birkhoffian system are established. The condition under which the form invariance can lead to a non-Noether conserved quantity and the form of the conserved quantity are deduced by relying on the total time derivative along the trajectory of the equations, and two corollaries in special cases are presented. An example is finally given to illustrate the application of the results.

关键词: Birkhoffian system, form invariance, non-Noether conserved quantity

Abstract: Based on the invariance of Birkhoffian equations under the infinitesimal transformations of groups, the definition and the criterion of a form invariance for a Birkhoffian system are established. The condition under which the form invariance can lead to a non-Noether conserved quantity and the form of the conserved quantity are deduced by relying on the total time derivative along the trajectory of the equations, and two corollaries in special cases are presented. An example is finally given to illustrate the application of the results.

Key words: Birkhoffian system, form invariance, non-Noether conserved quantity

中图分类号:  (Lie algebras of Lie groups)

  • 02.20.Sv
02.30.Hq (Ordinary differential equations)