Velocity-dependent symmetries and non-Noether conserved quantities of electromechanical systems  

作　　者：FU JingLi CHEN BenYong FU Hao ZHAO GangLing LIU RongWan ZHU ZhiYan 

机构地区：[1]Institute of Mathematical Physics,Zhejiang Sci-Tech University,Hangzhou c. China [2]Faculty of Mechanical Engineering & Automation,Zhejiang Sci-Tech University,Hangzhou 310018,China [3]China Jingye Engineering Corporation Limited Shenzhen Branch.Shenzhen 518054,China [4]Shanghai University, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072 China [5]Department of Physics,Shaoguan University,Shaoguan 512005,China

出　　处：《Science China(Physics,Mechanics & Astronomy)》2011年第2期288-295,共8页中国科学：物理学、力学、天文学（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant Nos.10672143 and 11072218)

摘　　要：The theory of velocity-dependent symmetries(or Lie symmetry) and non-Noether conserved quantities are presented corresponding to both the continuous and discrete electromechanical systems.Firstly,based on the invariance of Lagrange-Maxwell equations under infinitesimal transformations with respect to generalized coordinates and generalized charge quantities,the definition and the determining equations of velocity-dependent symmetry are obtained for continuous electromechanical systems;the Lie's theorem and the non-Noether conserved quantity of this symmetry are produced associated with continuous electromechanical systems.Secondly,the operators of transformation and the operators of differentiation are introduced in the space of discrete variables;a series of commuting relations of discrete vector operators are defined.Thirdly,based on the invariance of discrete Lagrange-Maxwell equations under infinitesimal transformations with respect to generalized coordinates and generalized charge quantities,the definition and the determining equations of velocity-dependent symmetry are obtained associated with discrete electromechanical systems;the Lie's theorem and the non-Noether conserved quantity are proved for the discrete electromechanical systems.This paper has shown that the discrete analogue of conserved quantity can be directly demonstrated by the commuting relation of discrete vector operators.Finally,an example is discussed to illustrate the results.The theory of velocity-dependent symmetries（or Lie symmetry） and non-Noether conserved quantities are presented corresponding to both the continuous and discrete electromechanical systems.Firstly,based on the invariance of Lagrange-Maxwell equations under infinitesimal transformations with respect to generalized coordinates and generalized charge quantities,the definition and the determining equations of velocity-dependent symmetry are obtained for continuous electromechanical systems; the Lie＇s theorem and the non-Noether conserved quantity of this symmetry are produced associated with continuous electromechanical systems.Secondly,the operators of transformation and the operators of differentiation are introduced in the space of discrete variables; a series of commuting relations of discrete vector operators are defined.Thirdly,based on the invariance of discrete Lagrange-Maxwell equations under infinitesimal transformations with respect to generalized coordinates and generalized charge quantities,the definition and the determining equations of velocity-dependent symmetry are obtained associated with discrete electromechanical systems; the Lie＇s theorem and the non-Noether conserved quantity are proved for the discrete electromechanical systems.This paper has shown that the discrete analogue of conserved quantity can be directly demonstrated by the commuting relation of discrete vector operators.Finally,an example is discussed to illustrate the results.

关 键 词：velocity-dependent symmetry conserved quantity DISCRETE electromechanical system 

分 类 号：O316[理学—一般力学与力学基础] TP271.4[理学—力学]