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
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
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.
Received: 11 November 2004
Revised: 17 May 2005
Accepted manuscript online:
PACS:
45.05.+x
(General theory of classical mechanics of discrete systems)
Fund: Project supported by the Heilongjiang
Natural Science Foundation of China (Grant No 9507).
Cite this article:
Qiao Yong-Fen (乔永芬), Li Ren-Jie (李仁杰), Sun Dan-Na (孙丹娜) Exact invariants and adiabatic invariants of Raitzin's canonical equations of motion for a nonlinear nonholonomic mechanical system 2005 Chinese Physics 14 1919
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