Inverse Problem of Lie Symmetries of Nonholonomic Variable Mass Systems

According to a know conserved quantity, the inverse problem of Lie symmetries of the nonholonomic mechanical systems with variant mass is considered, and the corresponding Lie symmetry is found out. For this, Noether symmetry corresponding to the given conserved quantity need to be found by Noether theory, then examining the symmetry if it is or not Lie symmetry according to the determining equations and restriction equations. The nonholonomic mechanical systems with variant mass that having Chetaev s type or non-Chetaev s type constraints are studied.