中国物理B ›› 2009, Vol. 18 ›› Issue (9): 3647-3650.doi: 10.1088/1674-1056/18/9/007

• GENERAL • 上一篇    下一篇

Lagrange--Noether method for solving second-order differential equations

吴惠彬1, 吴润衡2   

  1. (1)Faculty of Science, Beijing Institute of Technology, Beijing 100081, China; (2)Faculty of Science, North China University of Technology, Beijing 100041, China
  • 收稿日期:2008-07-01 修回日期:2008-10-18 出版日期:2009-09-20 发布日期:2009-09-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10272021 and 10572021), the Doctoral Program Foundation of Institution of Higher Education of China (Grant No 20040007022), and the Fund for Fundamental Research of BIT (Grant No 20070742005).

Lagrange--Noether method for solving second-order differential equations

Wu Hui-Bin(吴惠彬)a)† and Wu Run-Heng(吴润衡)b)   

  1. a Faculty of Science, Beijing Institute of Technology, Beijing 100081, China; b Faculty of Science, North China University of Technology, Beijing 100041, China
  • Received:2008-07-01 Revised:2008-10-18 Online:2009-09-20 Published:2009-09-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10272021 and 10572021), the Doctoral Program Foundation of Institution of Higher Education of China (Grant No 20040007022), and the Fund for Fundamental Research of BIT (Grant No 20070742005).

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摘要： The purpose of this paper is to provide a new method called the Lagrange--Noether method for solving second-order differential equations. The method is, firstly, to write the second-order differential equations completely or partially in the form of Lagrange equations, and secondly, to obtain the integrals of the equations by using the Noether theory of the Lagrange system. An example is given to illustrate the application of the result.

Abstract: The purpose of this paper is to provide a new method called the Lagrange--Noether method for solving second-order differential equations. The method is, firstly, to write the second-order differential equations completely or partially in the form of Lagrange equations, and secondly, to obtain the integrals of the equations by using the Noether theory of the Lagrange system. An example is given to illustrate the application of the result.

Key words: differential equation, Lagrange equation, Noether theory, integral

中图分类号:  (Partial differential equations)

  • 02.30.Jr
02.20.Rt (Discrete subgroups of Lie groups) 02.30.Rz (Integral equations)