Perturbation to symmetries and adiabatic invariants of a type of nonholonomic singular system

doi:10.1088/1009-1963/12/12/002

中国物理B ›› 2003, Vol. 12 ›› Issue (12): 1349-1353.doi: 10.1088/1009-1963/12/12/002

Perturbation to symmetries and adiabatic invariants of a type of nonholonomic singular system

陈向炜, 李彦敏

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

收稿日期:2003-04-15 修回日期:2003-05-27 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.

Perturbation to symmetries and adiabatic invariants of a type of nonholonomic singular system

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

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

Received:2003-04-15 Revised:2003-05-27 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.

摘要/Abstract

摘要： Based on the theory of symmetries and conserved quantities, the perturbation to the symmetries and adiabatic invariants of a type of nonholonomic singular system are discussed. Firstly, the concept of higher order adiabatic invariants of the system is proposed. Secondly, the conditions for existence of the exact invariants and adiabatic invariants are proved, and their forms are given. Thirdly, we study the inverse problems of the perturbation to symmetries of the system. An example is presented to illustrate these results.

Abstract: Based on the theory of symmetries and conserved quantities, the perturbation to the symmetries and adiabatic invariants of a type of nonholonomic singular system are discussed. Firstly, the concept of higher order adiabatic invariants of the system is proposed. Secondly, the conditions for existence of the exact invariants and adiabatic invariants are proved, and their forms are given. Thirdly, we study the inverse problems of the perturbation to symmetries of the system. An example is presented to illustrate these results.

Key words: nonholonomic singular system, perturbation to symmetry, exact invariant, adiabatic invariant

中图分类号: (Inverse problems)

02.30.Zz

02.30.Jr (Partial differential equations)

陈向炜, 李彦敏. Perturbation to symmetries and adiabatic invariants of a type of nonholonomic singular system[J]. 中国物理B, 2003, 12(12): 1349-1353.

Chen Xiang-Wei (陈向炜), Li Yan-Min (李彦敏). Perturbation to symmetries and adiabatic invariants of a type of nonholonomic singular system[J]. Chinese Physics, 2003, 12(12): 1349-1353.

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Perturbation to symmetries and adiabatic invariants of a type of nonholonomic singular system

Perturbation to symmetries and adiabatic invariants of a type of nonholonomic singular system

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