Lie symmetries, perturbation to symmetries and adiabatic invariants of Poincaré equations

doi:10.1088/1009-1963/15/3/002

中国物理B ›› 2006, Vol. 15 ›› Issue (3): 470-474.doi: 10.1088/1009-1963/15/3/002

Lie symmetries, perturbation to symmetries and adiabatic invariants of Poincaré equations

陈向炜, 刘翠梅, 李彦敏

Department of Physics, Shangqiu Teachers College, Shangqiu 476000, China

收稿日期:2005-10-25 修回日期:2005-11-01 出版日期:2006-03-20 发布日期:2006-03-20
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No 10372053) and the Natural Science Foundation of Henan Province, China (Grant No 0311010900).

Lie symmetries, perturbation to symmetries and adiabatic invariants of Poincaré equations

Chen Xiang-Wei (陈向炜), Liu Cui-Mei (刘翠梅), Li Yan-Min (李彦敏)

Department of Physics, Shangqiu Teachers College, Shangqiu 476000, China

Received:2005-10-25 Revised:2005-11-01 Online:2006-03-20 Published:2006-03-20
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No 10372053) and the Natural Science Foundation of Henan Province, China (Grant No 0311010900).

摘要/Abstract

摘要： Based on the invariance of differential equations under infinitesimal transformations, Lie symmetry, laws of conservations, perturbation to the symmetries and adiabatic invariants of Poincaré equations are presented.The concepts of Lie symmetry and higher order adiabatic invariants of Poincar\'{e} equations are proposed. The conditions for existence of the exact invariants and adiabatic invariants are proved, and their forms are also given. In addition, an example is presented to illustrate these results.

关键词: Poincaré equations, perturbation to symmetry, exact invariant, adiabatic invariant

Abstract: Based on the invariance of differential equations under infinitesimal transformations, Lie symmetry, laws of conservations, perturbation to the symmetries and adiabatic invariants of Poincaré equations are presented.The concepts of Lie symmetry and higher order adiabatic invariants of Poincaré equations are proposed. The conditions for existence of the exact invariants and adiabatic invariants are proved, and their forms are also given. In addition, an example is presented to illustrate these results.

Key words: Poincaré equations, perturbation to symmetry, exact invariant, adiabatic invariant

中图分类号: (Partial differential equations)

02.30.Jr

02.30.Hq (Ordinary differential equations) 02.20.-a (Group theory)

陈向炜, 刘翠梅, 李彦敏. Lie symmetries, perturbation to symmetries and adiabatic invariants of Poincaré equations[J]. 中国物理B, 2006, 15(3): 470-474.

Chen Xiang-Wei (陈向炜), Liu Cui-Mei (刘翠梅), Li Yan-Min (李彦敏). Lie symmetries, perturbation to symmetries and adiabatic invariants of Poincaré equations[J]. Chinese Physics, 2006, 15(3): 470-474.

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Lie symmetries, perturbation to symmetries and adiabatic invariants of Poincaré equations

Lie symmetries, perturbation to symmetries and adiabatic invariants of Poincaré equations

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