Lie Symmetries and Conserved Quantities of Holonomic Mechanical Systems in Terms of Quasi-Coordinatee

Aim To study the Lie symmetries and conserved quantities of holonomic mechanical systems in terms of qnasi-coordinates. Methods The definition of an infinitesimal generator for the holonomic mechanical systems in terms of quasi-coordinates was given. Lie's method of the invariance of ordinary differential equations under infinitesimal transformations was used. Results and Conclusion The determining equations of the Lie symmetries of holonomic mechanical systems in terms of quassi-coordinates are established. The structure equation and the form of conserved quantities are obtained. An example to illustrate the applicaiton of the result is given.