On the Nonholonomic Routh Sphere in a Magnetic Field

    2020, Volume 25, Number 1, pp.  18-32

    Author(s): Borisov A. V., Tsiganov A. V.

    This paper is concerned with the motion of an unbalanced dynamically symmetric sphere rolling without slipping on a plane in the presence of an external magnetic field. It is assumed that the sphere can consist completely or partially of dielectric, ferromagnetic, superconducting and crystalline materials. According to the existing phenomenological theory, the analysis of the sphere’s dynamics requires in this case taking into account the Lorentz torque, the Barnett – London effect and the Einstein – de Haas effect. Using this mathematical model, we have obtained conditions for the existence of integrals of motion which allow one to reduce integration of the equations of motion to a quadrature similar to the Lagrange quadrature for a heavy rigid body.
    Keywords: nonholonomic systems, integrable systems, magnetic field, Barnett – London effect, Einstein – de Haas effect
    Citation: Borisov A. V., Tsiganov A. V., On the Nonholonomic Routh Sphere in a Magnetic Field, Regular and Chaotic Dynamics, 2020, Volume 25, Number 1, pp. 18-32

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