中国物理B ›› 2004, Vol. 13 ›› Issue (10): 1615-1619.doi: 10.1088/1009-1963/13/10/006

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Lie symmetries and invariants of constrained Hamiltonian systems

刘荣万1, 陈立群2   

  1. (1)Department of Physics, Shaoguan University, Shaoguan 512005, China; Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; (2)Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
  • 收稿日期:2003-12-30 修回日期:2004-05-31 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 19972010).

Lie symmetries and invariants of constrained Hamiltonian systems

Liu Rong-Wan (刘荣万)ab, Chen Li-Qun (陈立群)b   

  1. a Department of Physics, Shaoguan University, Shaoguan 512005, China; b Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
  • Received:2003-12-30 Revised:2004-05-31 Online:2004-10-20 Published:2005-06-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 19972010).

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摘要： According to the theory of the invariance of ordinary differential equations under the infinitesimal transformations of group, the relations between Lie symmetries and invariants of the mechanical system with a singular Lagrangian are investigated in phase space. New dynamical equations of the system are given in canonical form and the determining equations of Lie symmetry transformations are derived. The proposition about the Lie symmetries and invariants are presented. An example is given to illustrate the application of the result in this paper.

关键词: analytical mechanics, constrained Hamilton system, Lie symmetry, invariant

Abstract: According to the theory of the invariance of ordinary differential equations under the infinitesimal transformations of group, the relations between Lie symmetries and invariants of the mechanical system with a singular Lagrangian are investigated in phase space. New dynamical equations of the system are given in canonical form and the determining equations of Lie symmetry transformations are derived. The proposition about the Lie symmetries and invariants are presented. An example is given to illustrate the application of the result in this paper.

Key words: analytical mechanics, constrained Hamilton system, Lie symmetry, invariant

中图分类号:  (Lie algebras of Lie groups)

  • 02.20.Sv
02.30.Hq (Ordinary differential equations) 03.65.Fd (Algebraic methods)