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Chinese Physics, 2007, Vol. 16(6): 1516-1520    DOI: 10.1088/1009-1963/16/6/004
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Perturbation to symmetries and Hojman adiabatic invariant for nonholonomic controllable mechanical systems with non-Chetaev type constraints

Xia Li-Li(夏丽莉) and Li Yuan-Cheng(李元成)
College of Physics Science and Technology, China University of Petroleum Dongying 257061, China
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.
Keywords:  nonholonomic controllable mechanical system      symmetry      perturbation      adiabatic invariant  
Received:  21 September 2006      Revised:  11 October 2006      Accepted manuscript online: 
PACS:  02.20.Qs (General properties, structure, and representation of Lie groups)  
  02.30.-f (Function theory, analysis)  
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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