中国物理B ›› 2005, Vol. 14 ›› Issue (1): 6-11.doi: 10.1088/1009-1963/14/1/002

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Localized Lie symmetries and conserved quantities for the finite-degree-of-freedom systems

白景华1, 傅景礼2, 陈立群3   

  1. (1)Department of Mathematics, Kaifeng University, Kaifeng,475000, China; (2)School of Natural Scence, Zhejiang University of Science,Hangzhou,310018, China;Shanghai Institute of Applied Mathematics and Mechanics,Shanghai University, Shanghai,200072, China; (3)Shanghai Institute of Applied Mathematics and Mechanics,Shanghai University, Shanghai,200072, China
  • 收稿日期:2003-10-31 修回日期:2004-09-08 出版日期:2005-01-20 发布日期:2005-01-20
  • 基金资助:
    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)

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    

  1. 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
  • Received:2003-10-31 Revised:2004-09-08 Online:2005-01-20 Published:2005-01-20
  • Supported by:
    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)

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摘要： 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.

关键词: localization Lie symmetry, infinite continuous group, conservation law, finite-degree-of freedom system

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.

Key words: localization Lie symmetry, infinite continuous group, conservation law, finite-degree-of freedom system

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  • 0320