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Noether-Mei symmetry of a discrete mechanico-electrical system

Chinese Physics B 2012年第11期21卷 14-19页

作者：张伟伟方建会 College of Science China University of Petroleum

Noether-Mei symmetry of a discrete mechanico-electrical system on a regular lattice is investigated. Firstly, the Noether symmetry of a discrete mechanico-electrical system is reviewed, and the motion equations and energy equations are derived. Secondly, the definition of Noether-Mei symmetry for the system is presented, and the criterion is derived. Thirdly, conserved quantities induced by Noether Mei symmetry with their existence conditions are obtained. Finally, an example is discussed to illustrate the results.

关键词： discrete mechanico-electrical system Noether-Mei symmetry conserved quantity

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Noether symmetries of discrete mechanico-electrical systems

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Chinese Physics B 2008年第12期17卷 4354-4360页

作者：傅景礼陈本永谢凤萍 Institute of Mathematical Physics Zhejiang Sci-Tech University Institute of Mechanical and Automatism Control Engineering Zhejiang Sci-Tech University

This paper focuses on studying Noether symmetries and conservation laws of the discrete mechanico-electricM systems with the nonconservative and the dissipative forces. Based on the invariance of discrete Hamilton action of the systems under the infinitesimal transformation with respect to the generalized coordinates, the generalized electrical quantities and time, it presents the discrete analogue of variational principle, the discrete analogue of Lagrange-Maxwell equations, the discrete analogue of Noether theorems for Lagrange Maxwell and Lagrange mechanico-electrical systems. Also, the discrete Noether operator identity and the discrete Noether-type conservation laws are obtained for these systems. An actual example is given to illustrate these results.

关键词： Noether symmetry conservation law discrete mechanico-electrical system dissipative function

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Noether conserved quantities and Lie point symmetries of difference Lagrange-Maxwell equations and lattices

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Chinese Physics B 2009年第7期18卷 2634-2641页

作者：傅景礼聂宁明黄健飞 Jiménez Salvador 唐贻发 Vzquez Luis 赵维加 Institute of Mathematical Physics Zhejiang Sci-Tech University State Key Laboratory of Scientific and Engineering Computing ICMSECAcademy of Mathematics and Systems ScienceChinese Academy of Sciences Department of Mathematics Qingdao University Departamento de Matema'tica Aplicada TTII E.T.S.I.Telecomunicacio'nUniversidad Polit'ecnica de Madrid28040-MadridSpain Departamento de Matemática Aplicada Facultad de MatemáticasInstituto de Matemática Interdisciplinar(IMI)Universidad Complutense de Madrid28040-MadridSpain Departamento de Matemática Aplicada Facultad de InformáticaInstituto de Matemática Interdisciplinar(IMI)Universidad Complutense de Madrid28040-MadridSpain

This paper presents a method to find Noether-type conserved quantities and Lie point symmetries for discrete mechanico-electrical dynamical systems,which leave invuriant the set of solutions of the corresponding difference scheme. This approach makes it possible to devise techniques for solving the Lagrange Maxwell equations in differences which correspond to mechanico-electrical systems,by adapting existing differential equations.In particular,it obtains a new systematic method to determine both the one-parameter Lie groups and the discrete Noether conserved quantities of Lie point symmetries for mechanico-electrical systems.As an application,it obtains the Lie point symmetries and the conserved quantities for the difference equation of a model that represents a capacitor microphone.

关键词： Lagrange Maxwell equation Lie point symmetry discrete mechanico-electrical system conserved quantity

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