The Motion of a Nonholonomic Chaplygin Sphere in a Magnetic Field, the Grioli Problem, and the Barnett-London Effect

摘要

In this paper, we consider the motion of a nonholonomic Chaplygin sphere on a plane in a constant magnetic field under the assumption that the sphere has dielectric and ferromagnetic properties. We also obtain a generalization of the integrable case thanks to V.V. Kozlov in the problem of the motion of a symmetric rigid body about a fixed point in a constant magnetic field and present a new particular integrable case of such motion.