中国物理B ›› 2008, Vol. 17 ›› Issue (6): 1957-1961.doi: 10.1088/1674-1056/17/6/004

• GENERAL • 上一篇    下一篇

Perturbation to Mei symmetry and Mei adiabatic invariants for mechanical systems in phase space

张明江, 方建会, 张小妮, 路凯   

  1. College of Physics Science and Technology, China University of Petroleum, Dongying 257061, China
  • 收稿日期:2007-08-17 修回日期:2007-09-24 出版日期:2008-06-20 发布日期:2008-06-20

Perturbation to Mei symmetry and Mei adiabatic invariants for mechanical systems in phase space

Zhang Ming-Jiang(张明江), Fang Jian-Hui(方建会)†, Zhang Xiao-Ni(张小妮), and Lu Kai(路凯)   

  1. College of Physics Science and Technology, China University of Petroleum, Dongying 257061, China
  • Received:2007-08-17 Revised:2007-09-24 Online:2008-06-20 Published:2008-06-20

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摘要： For a perturbed mechanical system in phase space, considering ${\tilde{{\rm d}}}/{ {{\rm d}t}}$ in the structure equation and process of proof including infinitesimal parameter $\varepsilon $ obviously, this paper studies the perturbation to Mei symmetry and adiabatic invariants. Firstly, the exact invariant induced directly from the Mei symmetry of the system without perturbation is given. Secondly, based on the concept of high-order adiabatic invariant, the determining equations of the perturbation to Mei symmetry are established, the condition of existence of the Mei adiabatic invariant led by the perturbation to Mei symmetry is obtained, and its form is presented. Lastly, an example is given to illustrate the application of the results.

Abstract: For a perturbed mechanical system in phase space, considering ${\tilde{{\rm d}}}/{ {{\rm d}t}}$ in the structure equation and process of proof including infinitesimal parameter $\varepsilon $ obviously, this paper studies the perturbation to Mei symmetry and adiabatic invariants. Firstly, the exact invariant induced directly from the Mei symmetry of the system without perturbation is given. Secondly, based on the concept of high-order adiabatic invariant, the determining equations of the perturbation to Mei symmetry are established, the condition of existence of the Mei adiabatic invariant led by the perturbation to Mei symmetry is obtained, and its form is presented. Lastly, an example is given to illustrate the application of the results.

Key words: Mei symmetry, perturbation, adiabatic invariant, mechanical system

中图分类号:  (Lagrangian and Hamiltonian mechanics)

  • 45.20.Jj
02.30.Jr (Partial differential equations)