The Integrable Problem of the Rolling Motion of a Dynamically Symmetric Spherical Top with One Nonholonomic Constraint

This paper addresses the problem of a sphere with axisymmetric mass distribution rolling on a horizontal plane. It is assumed that there is no slipping of the sphere as it rolls in the direction of the projection of the symmetry axis onto the supporting plane. It is also assumed that, in the direction perpendicular to the above-mentioned one, the sphere can slip relative to the plane. Examples of realization of the above-mentioned nonholonomic constraint are given. Equations of motion are obtained and their first integrals are found. It is shown that the system under consideration admits a redundant set of first integrals, which makes it possible to perform reduction to a system with one degree of freedom.