中国物理B ›› 2005, Vol. 14 ›› Issue (8): 1483-1485.doi: 10.1088/1009-1963/14/8/001

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Poisson structure and Casimir functions for a noncentral dynamical system in four-dimensional phase space

汪文珑1, 陈子栋2, 楼智美3   

  1. (1)Department of Mathematics, Shaoxing College of Arts and Sciences, Shaoxing 312000, China; (2)Department of Physics, Shaoxing College of Arts and Sciences,Shaoxing 312000, China; (3)Department of Physics, Shaoxing College of Arts and Sciences,Shaoxing 312000, China
  • 收稿日期:2005-02-06 修回日期:2005-03-15 出版日期:2005-07-13 发布日期:2005-07-13

Poisson structure and Casimir functions for a noncentral dynamical system in four-dimensional phase space

Lou Zhi-Mei (楼智美)a, Chen Zi-Dong (陈子栋)a, Wang Wen-Long (汪文珑)b    

  1. a Department of Physics, Shaoxing College of Arts and Sciences, Shaoxing 312000, China; b Department of Mathematics, Shaoxing College of Arts and Sciences, Shaoxing 312000, China
  • Received:2005-02-06 Revised:2005-03-15 Online:2005-07-13 Published:2005-07-13

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摘要： In this paper, we express the differential equations of a noncentral dynamical system in Ermakov formalism to obtain the Ermakov invariant. In term of Hamiltonian theories and using the Ermakov invariant as the Hamiltonian, the Poisson structure of a noncentral dynamical system in four-dimensional phase space are constructed. The result indicates that the Poisson structure is degenerate and the noncentral dynamical system possesses four invariants: the Hamiltonian, the Ermakov invariant and two Casimir functions.

关键词: noncentral dynamical system, Ermakov invariant, Poisson structure, Casimir functions

Abstract: In this paper, we express the differential equations of a noncentral dynamical system in Ermakov formalism to obtain the Ermakov invariant. In term of Hamiltonian theories and using the Ermakov invariant as the Hamiltonian, the Poisson structure of a noncentral dynamical system in four-dimensional phase space are constructed. The result indicates that the Poisson structure is degenerate and the noncentral dynamical system possesses four invariants: the Hamiltonian, the Ermakov invariant and two Casimir functions.

Key words: noncentral dynamical system, Ermakov invariant, Poisson structure, Casimir functions

中图分类号:  (Lagrangian and Hamiltonian mechanics)

  • 45.20.Jj
45.05.+x (General theory of classical mechanics of discrete systems)