Localized Lie symmetries and conserved quantities for the finite-degree-of-freedom systems
Fu Jing-Li (傅景礼)ab, Chen Li-Qun (陈立群)b, Bai Jing-Hua (白景华)c
a School of Natural Scence, Zhejiang University of Science,Hangzhou,310018, China; b Shanghai Institute of Applied Mathematics and Mechanics,Shanghai University, Shanghai,200072, China; c Department of Mathematics, Kaifeng University, Kaifeng,475000, China
Abstract This paper focuses on the study of localized Lie symmetries under the infinitesimal transformation of an infinite continuous group for the finite-degree-of-freedom systems. Based on an invariance of differential equation under an infinitesimal transformation, we present the localized Lie symmetries including direct and inverse problems for the finite degree-of-freedom mechanical systems. We also give the definitions,determining equations, structural equation and conserved laws of localized Lie symmetries, and further, the Lie symmetries under the infinitesimal transformation of a finite continuous group derived from localized Lie symmetry. Finally, an example is discussed to illustrate these results.
Received: 31 October 2003
Revised: 08 September 2004
Accepted manuscript online:
PACS:
0320
Fund: Project supported by the National Natural Science Foundation of China (Grant No 10372053) and the
Natural Science Foundation of Henan Province Government, China (Grant No 0311011400)
Cite this article:
Fu Jing-Li (傅景礼), Chen Li-Qun (陈立群), Bai Jing-Hua (白景华) Localized Lie symmetries and conserved quantities for the finite-degree-of-freedom systems 2005 Chinese Physics 14 6
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