On the first integrals of n-th order autonomous systems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:459

Article

Hu, Yanxia¹ 

[1] North China Elect Power Univ, Sch Math & Phys, Beijing 102206, Peoples R China

关键词: First integral;    Integrating factor;    Lie group;    n-th order autonomous system;   

DOI  :  10.1016/j.jmaa.2017.11.016

来源: Elsevier

【 摘 要 】

The first integrals of n-th order autonomous systems are considered. By getting integrating factors using n - 1 first integrals of the systems, a necessary condition on the existence of global first integrals of n-th order autonomous systems is presented. It is also proved that n - 1 functionally independent first integrals of an n-th order autonomous system can be obtained if the system possesses n - 1 functionally independent integrating factors. Based on one-parameter Lie groups admitted by n-th order autonomous systems, several methods to obtain first integrals of the systems are presented. Simultaneously, several related examples are given to illustrate the feasibility and the effectiveness of the proposed method. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free