中国物理B ›› 2004, Vol. 13 ›› Issue (10): 1611-1614.doi: 10.1088/1009-1963/13/10/005

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Lie symmetries and non-Noether conserved quantities for Hamiltonian canonical equations

谢凤萍1, 傅景礼2, 陈立群3   

  1. (1)Department of Applied Physics, Zhejiang University of Science, Hangzhou 310018, China; (2)Department of Applied Physics, Zhejiang University of Science, Hangzhou 310018, China; Shanghai University, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, China; (3)Department of Mechanics, Shanghai University, Shanghai 200072, China; Shanghai University, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, China
  • 收稿日期:2003-12-02 修回日期:2004-03-10 出版日期:2004-10-20 发布日期:2005-06-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10372053) and National Science Foundation of Henan Province, China (Grant No 0311011400).

Lie symmetries and non-Noether conserved quantities for Hamiltonian canonical equations

Fu Jing-Li (傅景礼)ac, Chen Li-Qun (陈立群)bc, Xie Feng-Ping (谢凤萍)a   

  1. a Department of Applied Physics, Zhejiang University of Science, Hangzhou 310018, China; b Shanghai University, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, China; c Shanghai University, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, China
  • Received:2003-12-02 Revised:2004-03-10 Online:2004-10-20 Published:2005-06-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10372053) and National Science Foundation of Henan Province, China (Grant No 0311011400).

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摘要： This paper focuses on studying Lie symmetries and non-Noether conserved quantities of Hamiltonian dynamical systems in phase space. Based on the infinitesimal transformations with respect to the generalized coordinates and generalized momenta, we obtain the determining equations and structure equation of the Lie symmetry for Hamiltonian dynamical systems. This work extends the research of non-Noether conserved quantity for Hamilton canonical equations, and leads directly to a new type of non-Noether conserved quantities of the systems. Finally, an example is given to illustrate these results.

关键词: Hamiltonian system, Lie symmetry, non-Noether conserved quantity, Lie groups

Abstract: This paper focuses on studying Lie symmetries and non-Noether conserved quantities of Hamiltonian dynamical systems in phase space. Based on the infinitesimal transformations with respect to the generalized coordinates and generalized momenta, we obtain the determining equations and structure equation of the Lie symmetry for Hamiltonian dynamical systems. This work extends the research of non-Noether conserved quantity for Hamilton canonical equations, and leads directly to a new type of non-Noether conserved quantities of the systems. Finally, an example is given to illustrate these results.

Key words: Hamiltonian system, Lie symmetry, non-Noether conserved quantity, Lie groups

中图分类号:  (Lie algebras of Lie groups)

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