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
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
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.
Received: 06 February 2005
Revised: 15 March 2005
Accepted manuscript online:
(General theory of classical mechanics of discrete systems)
Cite this article:
Lou Zhi-Mei (楼智美), Chen Zi-Dong (陈子栋), Wang Wen-Long (汪文珑) Poisson structure and Casimir functions for a noncentral dynamical system in four-dimensional phase space 2005 Chinese Physics 14 1483
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