A New Conservation Law Derived from Mei Symmetry for the System of Generalized Classical Mechanics

A new conservation theorem derived directly from Mei symmetry of the generalized classical mechanical system is presented. First, the differential equations of motion of the system are established, and the definition and criterion of Mei symmetry for the system of generalized classical mechanics are given, which are based upon the invariance of dynamical functions under infinitesimal transformations. Second, the condition under which a Mei symmetry can lead to a new conservation law is obtained and the form of the conservation law is presented. And finally, an example is given to illustrate the application of the results.