中国物理B ›› 2006, Vol. 15 ›› Issue (8): 1653-1661.doi: 10.1088/1009-1963/15/8/001

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Algebraic structure and Poisson's theory of mechanico-electrical systems

刘鸿基1, 傅景礼2, 唐贻发3   

  1. (1)Department of Physics, Shangqiu Teachers College, Shangqiu 476000, China; (2)Institute of Mathematical Physics, Zhejiang Sci-Tech University,Hangzhou 310018, China;Shanghai Institute of Applied Mathematics and Mechanics,Shanghai 200072, China; (3)State Key Laboratory of Scientific and Engineering Computing,Chinese Academy of Sciences, Beijing 100080, China
  • 收稿日期:2005-11-26 修回日期:2006-04-19 出版日期:2006-08-20 发布日期:2006-08-20
  • 基金资助:
    Project supported by the State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciences and the National Natural Science Foundation of China (Grant Nos 10471145 and 10372053) and the Natural Science Foundation of Henan Provincial Government of China (Grant Nos 0311011400 and 0511022200).

Algebraic structure and Poisson's theory of mechanico-electrical systems

Liu Hong-Ji(刘鸿基)a), Tang Yi-Fa(唐贻发)b), and Fu Jing-Li(傅景礼)c)d)†   

  1. a Department of Physics, Shangqiu Teachers College, Shangqiu 476000, China; b State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciences, Beijing 100080, China; c Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, Chinac Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, China
  • Received:2005-11-26 Revised:2006-04-19 Online:2006-08-20 Published:2006-08-20
  • Supported by:
    Project supported by the State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciences and the National Natural Science Foundation of China (Grant Nos 10471145 and 10372053) and the Natural Science Foundation of Henan Provincial Government of China (Grant Nos 0311011400 and 0511022200).

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摘要： The algebraic structure and Poisson's integral theory of mechanico-electrical systems are studied. The Hamilton canonical equations and generalized Hamilton canonical equations and their the contravariant algebraic forms for mechanico-electrical systems are obtained. The Lie algebraic structure and the Poisson's integral theory of Lagrange mechanico-electrical systems are derived. The Lie algebraic structure admitted and Poisson's integral theory of the Lagrange--Maxwell mechanico-electrical systems are presented. Two examples are presented to illustrate these results.

关键词: algebraic structure, Poisson integral method, mechanico-electrical system

Abstract: The algebraic structure and Poisson's integral theory of mechanico-electrical systems are studied. The Hamilton canonical equations and generalized Hamilton canonical equations and their the contravariant algebraic forms for mechanico-electrical systems are obtained. The Lie algebraic structure and the Poisson's integral theory of Lagrange mechanico-electrical systems are derived. The Lie algebraic structure admitted and Poisson's integral theory of the Lagrange--Maxwell mechanico-electrical systems are presented. Two examples are presented to illustrate these results.

Key words: algebraic structure, Poisson integral method, mechanico-electrical system

中图分类号:  (Algebraic structures and number theory)

  • 02.10.De
02.10.Ud (Linear algebra) 02.30.Rz (Integral equations) 03.50.De (Classical electromagnetism, Maxwell equations) 45.20.Jj (Lagrangian and Hamiltonian mechanics)