Abstract: Lie symmetries and conserved quantities of holonomic non-conservative dynamical systems in generalized classical mechanics were studied. First, the determining equations of Lie symmetries are established by using Lie's invariance method of infinitesimal transformations of differential equations. Second, the structure equations and the conserved quantities were obtained. Third, the inverse Lie symmetries system problems were discussed. Finally, an example to illustrate the application of the results was given.

Key words: conserved quantities , Lie symmetries, generalized mechanics system