Abstract This paper studies the perturbation to symmetries and adiabatic invariant for nonholonomic controllable mechanical systems with non-Chetaev type constraints. It gives the exact invariants introduced by the Lie symmetries of the nonholonomic controllable mechanical system with non-Chetaev type constraints without perturbation. Based on the definition of high-order adiabatic invariants of mechanical system, the perturbation of Lie symmetries for nonholonomic controllable mechanical system with non-Chetaev type constraints with the action of small disturbances is investigated, and a new type of adiabatic invariant of system are obtained. In the end of this paper, an example is given to illustrate the application of the results.
Received: 21 September 2006
Revised: 11 October 2006
Accepted manuscript online:
PACS:
02.20.Qs
(General properties, structure, and representation of Lie groups)
Fund: Project
supported by the Graduate Students' Innovative Foundation of China
University of Petroleum
(East China) (Grant No~S2006-31).
Cite this article:
Xia Li-Li(夏丽莉) and Li Yuan-Cheng(李元成） Perturbation to symmetries and Hojman adiabatic invariant for nonholonomic controllable mechanical systems with non-Chetaev type constraints 2007 Chinese Physics 16 1516
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