中国物理B ›› 2005, Vol. 14 ›› Issue (10): 1919-1925.doi: 10.1088/1009-1963/14/10/001

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Exact invariants and adiabatic invariants of Raitzin's canonical equations of motion for a nonlinear nonholonomic mechanical system

乔永芬1, 李仁杰2, 孙丹娜2   

  1. (1)Department of Mechanical Engineering and Automation, Zhejiang Institute of Science and Technology, Hangzhou 310018, China;Engineering College of Northeast Agricultural University,Harbin 150030, China;Faculty of Science Laiyang Agricultural College, Laiyang 265200, China; (2)Faculty of Science Laiyang Agricultural College, Laiyang 265200, China
  • 收稿日期:2004-11-11 修回日期:2005-05-17 出版日期:2005-10-20 发布日期:2005-10-20
  • 基金资助:
    Project supported by the Heilongjiang Natural Science Foundation of China (Grant No 9507).

Exact invariants and adiabatic invariants of Raitzin's canonical equations of motion for a nonlinear nonholonomic mechanical system

Qiao Yong-Fen (乔永芬)abc, Li Ren-Jie (李仁杰)c, Sun Dan-Na (孙丹娜)c   

  1. a Department of Mechanical Engineering and Automation, Zhejiang Institute of Science and Technology, Hangzhou 310018, Chinab Engineering College of Northeast Agricultural University, Harbin 150030, Chinac Faculty of Science Laiyang Agricultural College, Laiyang 265200, China
  • Received:2004-11-11 Revised:2005-05-17 Online:2005-10-20 Published:2005-10-20
  • Supported by:
    Project supported by the Heilongjiang Natural Science Foundation of China (Grant No 9507).

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摘要： The exact invariants and the adiabatic invariants of Raitzin's canonical equations of motion for a nonlinear nonholonomic mechanical system are studied. The relations between the invariants and the symmetries of the system are established. Based on the concept of higher-order adiabatic invariant of a mechanical system under the action of a small perturbation, the forms of the exact invariants and adiabatic invariants and the conditions for their existence are proved. Finally, the inverse problem of the perturbation to symmetries of the system is studied and an example is also given to illustrate the application of the results.

关键词: nonholonomic system, Raitzin's canonical equation, symmetry, perturbation, exact invariant, adiabatic invariant

Abstract: The exact invariants and the adiabatic invariants of Raitzin's canonical equations of motion for a nonlinear nonholonomic mechanical system are studied. The relations between the invariants and the symmetries of the system are established. Based on the concept of higher-order adiabatic invariant of a mechanical system under the action of a small perturbation, the forms of the exact invariants and adiabatic invariants and the conditions for their existence are proved. Finally, the inverse problem of the perturbation to symmetries of the system is studied and an example is also given to illustrate the application of the results.

Key words: nonholonomic system, Raitzin's canonical equation, symmetry, perturbation, exact invariant, adiabatic invariant

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

  • 45.05.+x
45.20.Jj (Lagrangian and Hamiltonian mechanics) 02.30.Zz (Inverse problems)