Lie Symmetries and Conserved Quantities of Third-Order Linear Nonholonomic Systems with Unilateral Constraint in a Phase Space

Lie symmetries and conserved quantities of third-order nonholonomic systems with unilateral constraint in phase space are studied. The determining equations and the restriction equations of the Lie symmetries of the systems are obtained, and the structural equations and the conserved quantities are given using the invariance of the ordinary differential equations under the infinitesimal transformations. The inverse problem of Lie symmetries of the systems is also studied, and an example is given to illustrate the application of the results.