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

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.