中国物理B ›› 2007, Vol. 16 ›› Issue (3): 570-577.doi: 10.1088/1009-1963/16/3/002

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Discrete variational principle and first integrals for Lagrange--Maxwell mechanico-electrical systems

萨尔瓦多·希梅尼斯1, 傅景礼2, 唐贻发3, 戴桂冬4   

  1. (1)Departamento de Matem\'atica Aplicada TTII, E.T.S.I. Telecomunicaci\'on, Universidad Polit\'ecnica de Madrid, 28040--Madrid, Spain; (2)Department of Physics, Zhejiang Sci-Tech University,Hangzhou 310018, China;State Key Laboratory of Scientific and Engineering Computing, ICMSEC,Academy of Mathematics and System Science,Chinese Academy of Sciences, Beijing 100080, China; (3)State Key Laboratory of Scientific and Engineering Computing, ICMSEC,Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing 100080, China; (4)State Key Laboratory of Scientific and Engineering Computing, ICMSEC,Academy of Mathematics and System Science,Chinese Academy of Sciences, Beijing 100080, China;Graduate School of the Chinese Academy of Sciences, Beijing 100080, China
  • 收稿日期:2005-09-21 修回日期:2006-09-14 出版日期:2007-03-20 发布日期:2007-03-20
  • 基金资助:
    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).

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)   

  1. 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
  • Received:2005-09-21 Revised:2006-09-14 Online:2007-03-20 Published:2007-03-20
  • Supported by:
    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).

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摘要： 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.

关键词: discrete, variational principle, first integral, mechanico-electrical systems

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.

Key words: discrete, variational principle, first integral, mechanico-electrical systems

中图分类号:  (Classical electromagnetism, Maxwell equations)

  • 03.50.De
02.30.Hq (Ordinary differential equations) 45.05.+x (General theory of classical mechanics of discrete systems) 45.20.Jj (Lagrangian and Hamiltonian mechanics)