Influence of Bartnett-London and Einstein-de Haas effects on the motion of the nonholonomic sphere of Routh. (Russian. English summary) Zbl 1479.37067
Summary: We consider the rolling of an unbalanced dynamically symmetric ball along a plane without slipping in the presence of an external magnetic field. We assume that the ball may be wholly or partially composed of dielectric, ferromagnetic, or superconducting materials. According to the existing phenomenological theory, in this case, when studying the dynamics of a ball, it is required to take into account the Lorentz force moment, Barnett-London moment, and Einstein-de Haas moment. Within the framework of this mathematical model, we obtain the conditions for the existence of integrals of motion, which allow us to reduce the integration of equations of motion to a quadrature similar to the Lagrange quadrature for a heavy rigid body.
MSC:
| 37J60 | Nonholonomic dynamical systems |
| 70F25 | Nonholonomic systems related to the dynamics of a system of particles |
| 74F15 | Electromagnetic effects in solid mechanics |
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