中国物理B ›› 2004, Vol. 13 ›› Issue (7): 979-983.doi: 10.1088/1009-1963/13/7/001

• •    下一篇

Characteristic functional structure of infinitesimal symmetry transformations of Birkhoffian systems

顾书龙1, 张宏彬2   

  1. (1)Department of Physics, Chaohu College, Chaohu 238000, China; (2)Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
  • 收稿日期:2003-10-16 修回日期:2004-01-16 出版日期:2004-07-05 发布日期:2005-07-05
  • 基金资助:
    Project supported by the Science Research Foundation of the Education Bureau of Anhui Province, China (Grant No 2004KJ294).

Characteristic functional structure of infinitesimal symmetry transformations of Birkhoffian systems

Gu Shu-Long (顾书龙)a, Zhang Hong-Bin (张宏彬)b   

  1. a Department of Physics, Chaohu College, Chaohu 238000, China; b Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
  • Received:2003-10-16 Revised:2004-01-16 Online:2004-07-05 Published:2005-07-05
  • Supported by:
    Project supported by the Science Research Foundation of the Education Bureau of Anhui Province, China (Grant No 2004KJ294).

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摘要： In this paper, it is shown that infinitesimal symmetry transformations of Birkhoffian systems have a characteristic functional structure, which is formulated by means of an auxiliary symmetry transformation function Z_μ(t,a) (introduced by the relation ξ_μ(t,a)=Z_μ(t,a)+\dot{a}^μξ_0 (t, a)) and is manifestly dependent upon the constants of motion of the system. At the end of the paper, an example is given to illustrate the application of the results.

关键词: analytical mechanics, Birkhoffian system, constant of motion, characteristic functional structure, infinitesimal symmetry transformation

Abstract: In this paper, it is shown that infinitesimal symmetry transformations of Birkhoffian systems have a characteristic functional structure, which is formulated by means of an auxiliary symmetry transformation function $Z_{\mu}(t,a)$ (introduced by the relation $\xi_{\mu}(t,a)=Z_{\mu}(t,a)+\dot{a}^{\mu}\xi_0 (t, a))$ and is manifestly dependent upon the constants of motion of the system. At the end of the paper, an example is given to illustrate the application of the results.

Key words: analytical mechanics, Birkhoffian system, constant of motion, characteristic functional structure, infinitesimal symmetry transformation

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

  • 45.05.+x
02.30.Sa (Functional analysis)