Velocity-dependent symmetries and conserved quantities of the constrained dynamical systems
Fu Jing-Li (傅景礼)ab, Chen Li-Qun (陈立群)b, Yang Xiao-Dong (杨晓东)b
a Institute of Mathematical Mechanics and Mathematical Physics of Shangqiu Teachers College, China; b Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
Abstract In this paper, we have extended the theorem of the velocity-dependent symmetries to nonholonomic dynamical systems. Based on the infinitesimal transformations with respect to the coordinates, we establish the determining equations and restrictive equation of the velocity-dependent system before the structure equation is obtained. The direct and the inverse issues of the velocity-dependent symmetries for the nonholonomic dynamical system is studied and the non-Noether type conserved quantity is found as the result. Finally, we give an example to illustrate the conclusion.
Received: 28 May 2003
Revised: 13 October 2003
Accepted manuscript online:
Fund: Project supported by the National Natural Science Foundation of China (Grant No 10372053) and the Natural Science Foundation of Henan Province, China (Grant No 0311011400).
Cite this article:
Fu Jing-Li (傅景礼), Chen Li-Qun (陈立群), Yang Xiao-Dong (杨晓东) Velocity-dependent symmetries and conserved quantities of the constrained dynamical systems 2004 Chinese Physics 13 287
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