The conservation theorem and the symmetries for systems of generalized classical mechanics are studied. In terms of the invariance of the ordinary differential equations under the infinitesimal transformations, this paper established the Li e symmetrical transformations of the systems in the high-dimensional extended ph ase space, which only depend on the canonical variables, and a new type of conse rvation laws are directly obtained from the Lie symmetries of the systems. Actua lly, the conservation laws are the generalization of a conservation theorem of H ojman to generalized classical mechanics. Finally, an example is given to illust rate the application of the results.
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