中国物理B ›› 2006, Vol. 15 ›› Issue (6): 1134-1136.doi: 10.1088/1009-1963/15/6/002

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First integrals and stability of second-order differential equations

梅凤翔1, 许学军2   

  1. (1)Department of Mechanics, Beijing Institute of Technology,Beijing 100081, China; (2)Department of Physics, Zhejiang Normal University, Jinhua 321004, China
  • 收稿日期:2005-10-12 修回日期:2006-02-21 出版日期:2006-06-20 发布日期:2006-06-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10572021) and the Doctoral Program Foundation of Institutions of Higher Education of China (Grant No 20040007022).

First integrals and stability of second-order differential equations

Xu Xue-Jun (许学军)a, Mei Feng-Xiang (梅凤翔)b    

  1. a Department of Physics, Zhejiang Normal University, Jinhua 321004, China; b Department of Mechanics, Beijing Institute of Technology, Beijing 100081, China
  • Received:2005-10-12 Revised:2006-02-21 Online:2006-06-20 Published:2006-06-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10572021) and the Doctoral Program Foundation of Institutions of Higher Education of China (Grant No 20040007022).

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摘要： The stability of second-order differential equations is studied by using their integrals. A system of second-order differential equations can be considered as a mechanical system with holonomic constraints. A conserved quantity of the mechanical system or a part of the system is obtained by using the Noether theory. It is possible that the conserved quantity becomes a Liapunov function and the stability of the system is proved by the Liapunov theorem.

关键词: differential equation, stability, Liapunov function, Noether theorem

Abstract: The stability of second-order differential equations is studied by using their integrals. A system of second-order differential equations can be considered as a mechanical system with holonomic constraints. A conserved quantity of the mechanical system or a part of the system is obtained by using the Noether theory. It is possible that the conserved quantity becomes a Liapunov function and the stability of the system is proved by the Liapunov theorem.

Key words: differential equation, stability, Liapunov function, Noether theorem

中图分类号:  (Partial differential equations)

  • 02.30.Jr
02.30.Cj (Measure and integration) 02.30.Sa (Functional analysis)