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Year
2019
Volume
29
Issue
4
Pages
583-598
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Section Mechanics
Title Influence of Bartnett-London and Einstein-de Haas effects on the motion of the nonholonomic sphere of Routh
Author(-s) Borisov A.V.a, Tsiganov A.V.a
Affiliations Steklov Mathematical Institute, Russian Academy of Sciencesa
Abstract 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.
Keywords nonholonomic systems, magnetic field, integrable systems
UDC 531.011, 537.634
MSC 37J60, 70F25, 74F15
DOI 10.20537/vm190409
Received 1 November 2019
Language Russian
Citation Borisov A.V., Tsiganov A.V. Influence of Bartnett-London and Einstein-de Haas effects on the motion of the nonholonomic sphere of Routh, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2019, vol. 29, issue 4, pp. 583-598.
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