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

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 Lies 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, t he definition and the determining equations of velocity-dependent symmetry are obtained associated with discrete electromechanical systems; the Lies 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

作者: FU JingLi CHEN BenYong FU Hao ZHAO GangLing LIU RongWan & ZHU ZhiYan

作者单位: Institute of Mathematical Physics. Zhejiang Sci-Tech University, Hangzhou 310018, China Faculty of Mechanical Engineering & Automation. Zhejiang Sci-Tech University, Hangzhou 310018, China China Jingye Engineering Corporation Limited Shenzhen Branch, Shenzhen 518054,China Shanghai University. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, China Department of Physics, Shaoguan University, Shaoguan 512005, China

会议类型: 国际会议

会议名称: 原子核磁矩国际研讨会

会议地点: 北京

会议语种:英文

页码: 288-295

在线出版日期: 2010-04-27（万方平台首次上网日期，不代表论文的发表时间）