Lie symmetries and conserved quantities of holonomic systems with remainder coordinates

To study the Lie symmetries and the conserved quantities of the holonomic systems with remainder coordinates, the invariance of the ordinary differential equations under the infinitesimal transformations was used to establish the determining equations and the restriction equations of the Lie symmetries of the systems. The structure equation and the form of conserved quantities were obtained. An example was given to illustrate the application of the result.