Lie symmetries theorem and its inverse of generalized mechanical systems in terms of quasi-coordinates

In this paper, Lie symmetries and conserved quantities of generalized mecha nical systems in terms of quasi-coordinates were studied. First, the defini tion of an infinitesimal generator for the generalized mechanical systems i n terms of quasi-coordinates were given, then the determining equations of the Lie symmetries were established by using Lie's method of invariance of ordinary differential equations under infinitesimal transformations. Next, the structure equation and the form of conserved quantities were obtained. Finally, the inverse problem of Lie symmetries systems were discussed and a n example to illustrate the application of the result was given.