中国物理B ›› 2003, Vol. 12 ›› Issue (9): 936-939.doi: 10.1088/1009-1963/12/9/302

• GENERAL • 上一篇    下一篇

Exact invariants and adiabatic invariants of the singular Lagrange system

陈向炜, 李彦敏   

  1. Department of Physics, Shangqiu Teachers College, Shangqiu 476000, China
  • 收稿日期:2003-02-21 修回日期:2003-03-13 出版日期:2005-03-16 发布日期:2005-03-16
  • 基金资助:
    Project supported by the Natural Science Foundation of Henan Province, China (Grant No 0311010900), and the Foundation of Young Key Member of the Teachers in Institutions of Higher Learning of Henan Province, China.

Exact invariants and adiabatic invariants of the singular Lagrange system

Chen Xiang-Wei (陈向炜), Li Yan-Min (李彦敏)   

  1. Department of Physics, Shangqiu Teachers College, Shangqiu 476000, China
  • Received:2003-02-21 Revised:2003-03-13 Online:2005-03-16 Published:2005-03-16
  • Supported by:
    Project supported by the Natural Science Foundation of Henan Province, China (Grant No 0311010900), and the Foundation of Young Key Member of the Teachers in Institutions of Higher Learning of Henan Province, China.

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摘要： Based on the theory of symmetries and conserved quantities of the singular Lagrange system, the perturbations to the symmetries and adiabatic invariants of the singular Lagrange systems are discussed. Firstly, the concept of higher-order adiabatic invariants of the singular Lagrange system is proposed. Then, the conditions for the existence of the exact invariants and adiabatic invariants are proved, and their forms are given. Finally, an example is presented to illustrate these results.

Abstract: Based on the theory of symmetries and conserved quantities of the singular Lagrange system, the perturbations to the symmetries and adiabatic invariants of the singular Lagrange systems are discussed. Firstly, the concept of higher-order adiabatic invariants of the singular Lagrange system is proposed. Then, the conditions for the existence of the exact invariants and adiabatic invariants are proved, and their forms are given. Finally, an example is presented to illustrate these results.

Key words: singular Lagrange system, symmetry, exact invariant, adiabatic invariant

中图分类号:  (Lie algebras of Lie groups)

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