Abstract:
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.
This work was supported by the Russian Science Foundation (project no. 19-71-30012) and
carried out at the Steklov Mathematical Institute of the Russian Academy of Sciences.
\Bibitem{BorTsi20}
\by Alexey V. Borisov, Andrey V. Tsiganov
\paper On the Nonholonomic Routh Sphere in a Magnetic Field
\jour Regul. Chaotic Dyn.
\yr 2020
\vol 25
\issue 1
\pages 18--32
\mathnet{http://mi.mathnet.ru/rcd1047}
\crossref{https://doi.org/10.1134/S1560354720010049}
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This publication is cited in the following 2 articles:
Wei Fan, “High-temperature superconductivity mechanism and an alternative theoretical model of Maxwell's classical electromagnetism theory”, Mod. Phys. Lett. B, 2023
Kilin A.A., Pivovarova E.N., “Stability and Stabilization of Steady Rotations of a Spherical Robot on a Vibrating Base”, Regul. Chaotic Dyn., 25:6 (2020), 729–752
Citation in format AMSBIB
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