First integrals and stability of second-order differential equations
Xu Xue-Jun (许学军)a, Mei Feng-Xiang (梅凤翔)b
a Department of Physics, Zhejiang Normal University, Jinhua 321004, China; b Department of Mechanics, Beijing Institute of Technology, Beijing 100081, China
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.
Received: 12 October 2005
Revised: 21 February 2006
Accepted manuscript online:
Fund: 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).
Cite this article:
Xu Xue-Jun (许学军), Mei Feng-Xiang (梅凤翔) First integrals and stability of second-order differential equations 2006 Chinese Physics 15 1134
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