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 Chin. Phys., 2003, Vol. 12(7): 695-699    DOI: 10.1088/1009-1963/12/7/001
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# Lie symmetries and conserved quantities of controllable nonholonomic dynamical systems

Bai Jing-Huaa, Fu Jing-Lib, Chen Li-Qunc, Yang Xiao-Dongc
a Department of Mathematics, Kaifeng University, Kaifeng 475000, China; b Institute of Mathematical Mechanics and Mathematical Physics, Shangqiu Teachers College, Shangqiu 476000, China; Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; c Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
Abstract  This paper concentrates on studying the Lie symmetries and conserved quantities of controllable nonholonomic dynamical systems. Based on the infinitesimal transformation, we establish the Lie symmetric determining equations and restrictive equations and give three definitions of Lie symmetries before the structure equations and conserved quantities of the Lie symmetries are obtained. Then we make a study of the inverse problems. Finally, an example is presented for illustrating the results.
Keywords:  Lie symmetry      conserved law      control      nonholonomic dynamical systems
Received:  06 September 2002      Revised:  12 March 2003      Published:  16 March 2005
 PACS: 02.30.Hq (Ordinary differential equations) 02.30.Zz (Inverse problems) 02.20.Sv (Lie algebras of Lie groups)

#### Cite this article:

Bai Jing-Hua, Fu Jing-Li, Chen Li-Qun, Yang Xiao-Dong Lie symmetries and conserved quantities of controllable nonholonomic dynamical systems 2003 Chin. Phys. 12 695

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