基于微分变分原理研究相空间中非完整系统的守恒律

摘要

In order to find further the conservation laws of dynamical systems, in this paper, the conservation laws of nonholonomic systems in phase space by means of the differential variational principle are studied.Firstly, from the Hamilton principle of a nonconservative system, the differential variational principle for a nonholonomic nonconservative system in phase space is established.And then, through the introduction of generalized variational, the condition of invariance for the principle under the infinitesimal transformations is given. Finally, the conservation laws of the nonholonomic nonconservative mechanical system in phase space are obtained.Two examples are given to illustrate its application.%为了进一步寻求动力学系统的守恒律，文章基于微分变分原理研究相空间中非完整力学系统的守恒律。首先从非保守系统的Hamilton原理出发，建立了相空间中非完整非保守系统的微分变分原理；其次，通过引进广义变分，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，导出了相空间中非完整非保守力学系统的守恒律。文末举例说明结果的应用。