Bifurcation Analysis and Dynamical Phenomena in the Problem of the Rolling Motion of a Dynamically Symmetric Spherical Top with One Nonholonomic Constraint

In this paper, we address the problem of the rolling motion of a sphere with axisymmetric mass distribution on a horizontal plane. It is assumed that the sphere does not slip as it rolls in the direction of the projection of the symmetry axis onto the supporting plane. The system under consideration admits a redundant set of first integrals. This makes it possible to perform a reduction to a system with one degree of freedom and to write it in Hamiltonian form. In this paper we carry out a bifurcation analysis of the system under consideration. In particular, we perform a classification of possible types of motion according to values of the first integrals of motion and the mass-geometric parameters, and describe the singularities of the system and the dynamical phenomena observed near them.