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Chin. Phys. B, 2011, Vol. 20(3): 030202    DOI: 10.1088/1674-1056/20/3/030202
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Mei symmetries and Mei conserved quantities for higher-order nonholonomic constraint systems

Jiang Wen-An, Li Zhuang-Jun, Luo Shao-Kai
Institute of Mathematical Mechanics and Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China
Abstract  This paper presents the Mei symmetries and new types of non-Noether conserved quantities for a higher-order nonholonomic constraint mechanical system. On the basis of the form invariance of differential equations of motion for dynamical functions under general infinitesimal transformation, the determining equations, the constraint restriction equations and the additional restriction equations of Mei symmetries of the system are constructed. The criterions of Mei symmetries, weak Mei symmetries and strong Mei symmetries of the system are given. New types of conserved quantities, i.e. the Mei symmetrical conserved quantities, the weak Mei symmetrical conserved quantities and the strong Mei symmetrical conserved quantities of a higher-order nonholonomic system, are obtained. Then, a deduction of the first-order nonholonomic system is discussed. Finally, two examples are given to illustrate the application of the method and then the results.
Keywords:  higher-order nonholonomic system      Mei symmetry      Mei conserved quantity     
Received:  21 September 2010      Published:  15 March 2011
PACS:  02.20.Sv (Lie algebras of Lie groups)  
  11.30.-j (Symmetry and conservation laws)  
  03.50.Kk (Other special classical field theories)  
  11.10.Ef (Lagrangian and Hamiltonian approach)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 10372053).

Cite this article: 

Jiang Wen-An, Li Zhuang-Jun, Luo Shao-Kai Mei symmetries and Mei conserved quantities for higher-order nonholonomic constraint systems 2011 Chin. Phys. B 20 030202

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