On a nonholonomic dynamical problem (Q2473688)

The authors study the rolling motion of a ball under the assumption that its center of mass moves over an arbitrary cylindrical surface. The problem is considered as a nonholonomic dynamical problem. For the motion in gravity field it is proved that the system is a Poisson-Hamiltonian one, and a Casimir function is derived. A second integral is obtained by using Fourier series, which allows to prove that the system is Liouville integrable.