中国物理B ›› 2008, Vol. 17 ›› Issue (6): 1967-1971.doi: 10.1088/1674-1056/17/6/006

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Perturbation to Lie symmetry and another type of Hojman adiabatic invariants for Birkhoffian systems

方建会1, 丁宁2, 陈相霞3   

  1. (1)College of Physics Science and Technology, China University of Petroleum, Dongying 257061, China; (2)Department of Physics and Electronics Science, Binzhou University, Binzhou 256603, China; (3)Dezhou University, Dezhou 253023, China
  • 收稿日期:2007-10-24 修回日期:2008-01-08 出版日期:2008-06-20 发布日期:2008-06-20
  • 基金资助:
    Project partially supported by the Young Personnel Innovation Foundation of Binzhou University, China (Grant No BZXYQNLG200715) and the Experimentation and Technology Foundation of Binzhou University, China (Grant No BZXYSYXM200702).

Perturbation to Lie symmetry and another type of Hojman adiabatic invariants for Birkhoffian systems

Ding Ning(丁宁)a)†, Fang Jian-Hui(方建会)b), and Chen Xiang-Xia(陈相霞)c)   

  1. a Department of Physics and Electronics Science, Binzhou University, Binzhou 256603, China; b College of Physics Science and Technology, China University of Petroleum, Dongying 257061, China; c Dezhou University, Dezhou 253023, China
  • Received:2007-10-24 Revised:2008-01-08 Online:2008-06-20 Published:2008-06-20
  • Supported by:
    Project partially supported by the Young Personnel Innovation Foundation of Binzhou University, China (Grant No BZXYQNLG200715) and the Experimentation and Technology Foundation of Binzhou University, China (Grant No BZXYSYXM200702).

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摘要： The perturbation to Lie symmetry and another type of Hojman adiabatic invariants induced from the perturbation to Lie symmetry for Birkhoffian systems are studied. The exact invariants of Lie symmetry for the system without perturbation are given. Based on the concept of adiabatic invariant, the perturbation to Lie symmetry is discussed and another new type of Hojman adiabatic invariants that have the different form from that in [{\em Acta Phys. Sin.} {\bf 55} 3833] for the perturbed system are obtained.

关键词: Lie symmetry, perturbation, Hojman adiabatic invariant, Birkhoffian system

Abstract: The perturbation to Lie symmetry and another type of Hojman adiabatic invariants induced from the perturbation to Lie symmetry for Birkhoffian systems are studied. The exact invariants of Lie symmetry for the system without perturbation are given. Based on the concept of adiabatic invariant, the perturbation to Lie symmetry is discussed and another new type of Hojman adiabatic invariants that have the different form from that in [Acta Phys. Sin. 55 3833] for the perturbed system are obtained.

Key words: Lie symmetry, perturbation, Hojman adiabatic invariant, Birkhoffian system

中图分类号:  (Lagrangian and Hamiltonian mechanics)

  • 45.20.Jj