中国物理B ›› 2005, Vol. 14 ›› Issue (12): 2391-2394.doi: 10.1088/1009-1963/14/12/003

• GENERAL • 上一篇    下一篇

Methods of analytical mechanics for solving differential equations of first order

吴惠彬, 梅凤翔   

  1. Faculty of Science, Beijing Institute of Technology,Beijing 100081, China
  • 收稿日期:2005-03-04 修回日期:2005-07-24 出版日期:2005-12-20 发布日期:2005-12-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10272021) and the Doctorate Foundation of the State Education Ministry of China (Grant No 20040007022).

Methods of analytical mechanics for solving differential equations of first order

Wu Hui-Bin (吴惠彬), Mei Feng-Xiang (梅凤翔)   

  1. Faculty of Science, Beijing Institute of Technology,Beijing 100081, China
  • Received:2005-03-04 Revised:2005-07-24 Online:2005-12-20 Published:2005-12-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10272021) and the Doctorate Foundation of the State Education Ministry of China (Grant No 20040007022).

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摘要： A differential equation of first order can be expressed by the equation of motion of a mechanical system. In this paper, three methods of analytical mechanics, i.e. the Hamilton--Noether method, the Lagrange--Noether method and the Poisson method, are given to solve a differential equation of first order, of which the way may be called the mechanical methodology in mathematics.

Abstract: A differential equation of first order can be expressed by the equation of motion of a mechanical system. In this paper, three methods of analytical mechanics, i.e. the Hamilton--Noether method, the Lagrange--Noether method and the Poisson method, are given to solve a differential equation of first order, of which the way may be called the mechanical methodology in mathematics.

Key words: analytical mechanics, differential equation, Noether theory, Poisson method

中图分类号:  (Partial differential equations)

  • 02.30.Jr
02.10.Ud (Linear algebra)