Integrating the equations of motion of a nonholonomic system by quadratures

Reference [1] points out that if a Hamiltonian system with n degrees of freedom hasn independent first integrals in involution, i.e. the Lie algebra is commutative, then it canbe integrated by quadratures. This note studies a particular nonholonomic system, theequations of whose motion can be transformed in the form of Hamilton’s canonical equa-tions. If a sufficiently large number of the independent first integrals in involution is ob-tained, then the above result used to study holonomic systems can be applied to