Symmetries and conserved quantities for systems of generalized classical mechanics

In this paper, the symmetries and the conserved quantities for systems of g eneralized classical mechanics are studied. First, the generalized Noether' s theorem and the generalized Noether's inverse theorem of the systems are given, which are based upon the invariant properties of the canonical actio n with respect to the action of the infinitesimal transformation of r-param eter finite group of transformation; second, the Lie symmetries and conserv ed quantities of the systems are studied in accordance with the Lie's theor y of the invariance of differential equations under the transformation of i nfinitesimal groups; and finally, the inner connection between the two kind s of symmetries of systems is discussed.