中文摘要：

以往关于约束动力学系统Tzénoff方程对称性和守恒量的研究,针对的都是一般Tzénoff方程,为了研究广义Tzénoff方程的Mei对称性和守恒量,首先建立了完整约束和非完整约束2种力学状态下的广义Tzénoff方程,给出了在群的无限小变换下Mei对称性的定义和判据,研究了Mei对称性产生守恒量的必要条件,给出了这种新守恒量的函数表达式和导出这种守恒量的条件方程,只要能找到规范函数满足条件方程,那么该系统就一定存在这种新守恒量.

英文摘要：

The previous research on the symmetry and conserved quantities of the restraint dynamics system Tzénoff equation has focused on the general Tzénoff equations.In order to explore the Mei symmetry and conservation quantities of the generalized Tzénoff equations,we have established the generalized Tzénoff equations in the two mechanics states of complete restraint and nonholonomic restraint firstly.The definition and criterion of the Mei symmetry under the group＇s infinitesimal transformation have been offered.Furthermore,the necessary condition of the conserved quantities produced by the Mei symmetry are researched and the function expression of the new conserved quantities and the conditional equation that derives the conserved quantities have been presented.As long as the standard function satisfying the conditional equation is found,the new conserved quantities invariably exist in this system.