利用单参数Lie群组的一种可解性求自治系统首次积分的方法  

Searching for First Integral of Autonomous System Based on a Kind of Solvability of One-parameter Lie Groups

作　　者：薛崇政[1] 胡彦霞[1] 

机构地区：[1]华北电力大学数理学院,北京102206

出　　处：《应用数学学报》2013年第4期738-747,共10页Acta Mathematicae Applicatae Sinica

基　　金：中央高校基本科研业务费专项资金(12MS87)资助项目

摘　　要：讨论了自治系统接受的单参数Lie群组具有一种可解性的情况下求系统的一个首次积分的具体方法.对于n阶自治系统,给出相应参数的一组确定取值,求得系统首次积分;对于三阶自治系统,当系统接受的单参数Lie群组可解时,验证求得首次积分的条件一定成立.The method for obtaining one first integral of autonomous systems accepting a series of one-parameter Lie groups with the solvability was discussed. For n-th order autonomous systems accepting n - 1 solvable one-parameter Lie groups, a specific method for obtaining first integrals by valuing the parameters was given. Specially, the method for obtaining first integrals of the third order autonomous systems accepting two solvable one- parameter Lie groups was discussed. Furthermore, the method for obtaining first integrals was proved to be right without any conditions.

关 键 词：自治系统 单参数Lie群组 可解性 首次积分 

分 类 号：O175.14[理学—数学]