广义经典力学系统的对称性与Mei守恒量

研究广义经典力学系统的对称性和一类新型守恒量——Mei守恒量.在高维增广相空间中建立 了系统的运动微分方程；给出了系统的Mei对称性、Noether对称性和Lie对称性的判据；得 到了分别由三种对称性导致Mei守恒量的条件和Mei守恒量的形式.举例说明结果的应用.关键词：广义经典力学Mei对称性Noether对称性Lie对称性守恒量

Symmetries and Mei conserved quantities for systems of generalized classical mechanics

In this paper, the symmetries and a new type of conserved quantities called Mei conserved quantities for systems of generalized classical mechanics are studied. In the high-dimensional extended phase space, the differential equations of motion of the systems are established, and the criteria for Mei symmetries, Noethe r symmetries and Lie symmetries of the systems are given. The conditions, under which the above three symmetries can respectively lead to the Mei conserved qu antities, and the form of the Mei conserved quantities are obtained. Finally, an example is given to illustrate the application of the results.