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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.