Lie symmetries and conserved quantities of non-holonomic mechanical systems with unilateral Vacco constraints

In this paper, we study the Lie symmetries and the conserved quantities of non-holonomic mechanical systems with unilateral Vacco constraints. We give the conditions and the form of conserved quantities due to the Lie symmetries of the systems, and present the inverse problem of the above problem, i.e. finding the corresponding Lie symmetry transformation according to a given integral of the system. Finally, we give an example to illustrate the application of the results.