基于微分变分原理研究相空间中非保守力学系统的守恒律

A study of conservation laws of nonconservative mechanical systems in phase space based on differential variational principle

基于微分变分原理研究相空间中非保守力学系统的守恒律。首先,利用Hamilton原理建立了相空间中非保守系统的微分变分原理;其次,给出了此微分变分原理在无限小变换下的不变性条件;最后,导出了相空间中非保守系统守恒律存在的条件及其形式。文章表明:利用微分变分原理也可以研究相空间中力学系统的守恒律。

This paper has studied the conservation laws of nonconservative mechanical systems in phase space based on the differential variational principle. Firstly, the differential variational principle for a nonconservative mechanical system in phase space was established by means of the Hamilton principle. Secondly, we gave the in-variance condition for the differential variational principle under the infinitesimal transformations. Finally, the condition and the form for the existence of the conservation laws of the nonconservative system in phase space were deduced. This paper suggests that the differential variational principles can also be used to study the con-servation laws of mechanical systems in phase space.