Integrating the equations of motion of a nonholonomic system by quadratures

摘要

Reference [1] points out that if a Hamiltonian system with n degrees of freedom has n independent first integrals in involution, i.e.. the Lie algebra is commutative, then it can be integrated by quadratures. This note studies a particular nonholonomic system, the equations of whose motion can be transformed in the form of Hamilton's canonical equations. If a sufficiently large number of the independent first integrals in involution is obtained, then the above result used to study holonomic systems can be applied to the nonholonomic system. Therefore, the problem in integration of the equations of motion of a nonholonomic system is solved.