中国物理B ›› 2001, Vol. 10 ›› Issue (11): 997-1000.doi: 10.1088/1009-1963/10/11/301

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EXACT AND ADIABATIC INVARIANTS OF FIRST-ORDER LAGRANGE SYSTEMS

尚玫1, 梅凤翔1, 陈向炜2   

  1. (1)Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, China; (2)Department of Physics, Shangqiu Teachers College, Shangqiu Henan 476000, China
  • 收稿日期:2001-04-20 修回日期:2001-05-26 出版日期:2001-11-15 发布日期:2005-06-12
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 19972010), and by the Natural Science Foundation of the Education Commission of Henan Province, China (Grant No.2000130003).

EXACT AND ADIABATIC INVARIANTS OF FIRST-ORDER LAGRANGE SYSTEMS

Chen Xiang-wei (陈向炜)a, Shang Mei (尚玫)b, Mei Feng-xiang (梅凤翔)b   

  1. a Department of Physics, Shangqiu Teachers College, Shangqiu Henan 476000, China; b Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, China
  • Received:2001-04-20 Revised:2001-05-26 Online:2001-11-15 Published:2005-06-12
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 19972010), and by the Natural Science Foundation of the Education Commission of Henan Province, China (Grant No.2000130003).

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

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

Key words: first-order Lagrange system, symmetry, exact invariant, adiabatic invariant

中图分类号:  (Ordinary differential equations)

  • 02.30.Hq