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
a Department of Physics, Shangqiu Teachers College, Shangqiu Henan 476000, China; b Department of Applied Mechanics, Beijing Institute of Technology, Beijing 100081, China
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.
Received: 20 April 2001
Revised: 26 May 2001
Accepted manuscript online:
PACS:
02.30.Hq
(Ordinary differential equations)
Fund: 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).
Cite this article:
Chen Xiang-wei (陈向炜), Shang Mei (尚玫), Mei Feng-xiang (梅凤翔) EXACT AND ADIABATIC INVARIANTS OF FIRST-ORDER LAGRANGE SYSTEMS 2001 Chinese Physics 10 997
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