Discrete variational principle and first integrals for Lagrange--Maxwell mechanico-electrical systems
Fu Jing-Li(傅景礼)a)b)†, Dai Gui-Dong(戴桂冬)b)d), Salvador Jimènez(萨尔瓦多·希梅尼斯)c), and Tang Yi-Fa(唐贻发)b)
a Department of Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China; b State Key Laboratory of Scientific and Engineering Computing, ICMSEC, Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing 100080, China; c Departamento de Matemática Aplicada TTII, E.T.S.I. Telecomunicación, Universidad Politécnica de Madrid, 28040–Madrid, Spain; d Graduate School of the Chinese Academy of Sciences, Beijing 100080, China
Abstract This paper presents a discrete variational principle and a method to build first-integrals for finite dimensional Lagrange--Maxwell mechanico-electrical systems with nonconservative forces and a dissipation function. The discrete variational principle and the corresponding Euler--Lagrange equations are derived from a discrete action associated to these systems. The first-integrals are obtained by introducing the infinitesimal transformation with respect to the generalized coordinates and electric quantities of the systems. This work also extends discrete Noether symmetries to mechanico-electrical dynamical systems. A practical example is presented to illustrate the results.
Received: 21 September 2005
Revised: 14 September 2006
Accepted manuscript online:
Fund: Project
supported by State Key Laboratory of Scientific and Engineering
Computing, Chinese Academy of Sciences and the National Natural
Science Foundation of China (Grant Nos~10672143 and 10471145)
and the Natural Science Foundation of Henan Province Government,
China (Grant Nos~0311011400 and 0511022200).
Cite this article:
Fu Jing-Li(傅景礼), Dai Gui-Dong(戴桂冬), Salvador Jimènez(萨尔瓦多·希梅尼斯), and Tang Yi-Fa(唐贻发) Discrete variational principle and first integrals for Lagrange--Maxwell mechanico-electrical systems 2007 Chinese Physics 16 570
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