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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2019, Volume 29, Issue 4, Pages 583–598 (Mi vuu703)  

MECHANICS

Influence of BartnettLondon and Einsteinde Haas effects on the motion of the nonholonomic sphere of Routh

A. V. Borisov, A. V. Tsiganov

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina, 8, Moscow, 119991, Russia

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.

Funding Agency Grant Number
Russian Science Foundation 19-71-30012
The study was funded by the Russian Science Foundation (project no. 19-71-30012).


DOI: https://doi.org/10.20537/vm190409

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Full text: http://vm.udsu.ru/.../2019-4-9
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Bibliographic databases:

UDC: 531.011, 537.634
MSC: 37J60, 70F25, 74F15
Received: 01.11.2019

Citation: A. V. Borisov, A. V. Tsiganov, “Influence of BartnettLondon and Einsteinde Haas effects on the motion of the nonholonomic sphere of Routh”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 29:4 (2019), 583–598

Citation in format AMSBIB
\Bibitem{BorTsi19}
\by A.~V.~Borisov, A.~V.~Tsiganov
\paper Influence of BartnettLondon and Einsteinde Haas effects on the motion of the nonholonomic sphere of Routh
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2019
\vol 29
\issue 4
\pages 583--598
\mathnet{http://mi.mathnet.ru/vuu703}
\crossref{https://doi.org/10.20537/vm190409}


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