Abstract: There are two kinds of modern methods in finding conservation laws. One is the Noether method which is based on the invariance of the Hamilton's action under the infinitesimal transformations, the other one is the Lie method which is based on the invariance of the differential equations under infinitesimal transformations. In mathematics, the symmetry methods in the theory of differential equations have made great progress in recent years. In mechanics, the research on Lie symmetries and conservation l...