Mei symmetry and new conserved quantities for non-material volumes

Abstract

This paper is focused on the Mei symmetry of non-material volumes. The Mei symmetrical definition and criterion are given. The criterion equations of the system are presented by introducing the invariance of dynamical functions of the system under infinitesimal transformations of Lie groups. The structure equations and the form of new conserved quantities are proposed. An example is given to illustrate the application of the method; a new conserved quantity is obtained under the Mei symmetrical transformations.