Exact invariants and adiabatic invariants of  holonomic system in terms of quasi-coordinates

doi:10.1088/1009-1963/14/4/005

中国物理B ›› 2005, Vol. 14 ›› Issue (4): 663-668.doi: 10.1088/1009-1963/14/4/005

Exact invariants and adiabatic invariants of holonomic system in terms of quasi-coordinates

陈向炜, 李彦敏

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

收稿日期:2004-10-10 修回日期:2004-11-02 出版日期:2005-03-28 发布日期:2005-03-28
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No 10372053); 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 holonomic system in terms of quasi-coordinates

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

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

Received:2004-10-10 Revised:2004-11-02 Online:2005-03-28 Published:2005-03-28
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No 10372053); 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.

摘要/Abstract

摘要： Based on the theory of Lie symmetries and conserved quantities, the exact invariants and adiabatic invariants of holonomic system are studied in terms of quasi-coordinates. The perturbation to symmetries for the holonomic system in terms of quasi-coordinates under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the form of exact invariants and adiabatic invariants as well as the conditions for their existence are given. Then the corresponding inverse problem is studied.

Abstract: Based on the theory of Lie symmetries and conserved quantities, the exact invariants and adiabatic invariants of holonomic system are studied in terms of quasi-coordinates. The perturbation to symmetries for the holonomic system in terms of quasi-coordinates under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the form of exact invariants and adiabatic invariants as well as the conditions for their existence are given. Then the corresponding inverse problem is studied.

Key words: holonomic system in terms of quasi-coordinates, perturbation, exact invariant, adiabatic invariant

中图分类号: (General theory of classical mechanics of discrete systems)

45.05.+x

02.30.Zz (Inverse problems) 45.40.Cc (Rigid body and gyroscope motion)

陈向炜, 李彦敏. Exact invariants and adiabatic invariants of holonomic system in terms of quasi-coordinates[J]. 中国物理B, 2005, 14(4): 663-668.

Chen Xiang-Wei (陈向炜), Li Yan-Min (李彦敏). Exact invariants and adiabatic invariants of holonomic system in terms of quasi-coordinates[J]. Chinese Physics, 2005, 14(4): 663-668.

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Exact invariants and adiabatic invariants of holonomic system in terms of quasi-coordinates

Exact invariants and adiabatic invariants of holonomic system in terms of quasi-coordinates

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