Noether-Lie Symmetry of Generalized Classical Mechanical Systems

In this paper, the Noether-Lie symmetry and conserved quantities of generalized classical mechanical system are studied. The definition and the criterion of the Noether-Lie symmetry for the system under the general infinitesimal transformations of groups are given. The Noether conserved quantity and the Hojman conserved quantity deduced from the Noether-Lie symmetry are obtained. An example is given to illustrate the application of the results.