Lie Symmetries of Holonomic Systems with Unilateral Constraints in Phase Space

Aim To study the Lie symmetries and the conserved quantities of holonomic systems with unilateral constraints in phase space. Methods The invariance of ordinary differential equations under the infinitesimal transformations was used to establish the determining equations and the restriction equations of the Lie symmetries of systems. Results and Conclusion The structure equations and the form of conserved quantities were obtained, and the solution of the inverse problem was presented. Two examples were given to illustrate the application of the results.