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Nelin. Dinam., 2019, Volume 15, Number 2, Pages 171–178 (Mi nd650)  

Nonlinear physics and mechanics

The Rolling of a Homogeneous Ball with Slipping on a Horizontal Rotating Plane

T. B. Ivanova

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

Abstract: This paper is concerned with the rolling of a homogeneous ball with slipping on a uniformly rotating horizontal plane. We take into account viscous friction forces arising when there is slipping at the contact point. It is shown that, as the coefficient of viscosity tends to infinity, the solution of the generalized problem on each fixed time interval tends to a solution of the corresponding nonholonomic problem.

Keywords: rotating surface, turntable, nonholonomic constraint, rolling ball, sliding, viscous friction

Funding Agency Grant Number
Russian Science Foundation 19-71-30012
This work is supported by the Russian Science Foundation under grant 19-71-30012 and performed in Steklov Mathematical Institute of Russian Academy of Sciences.


DOI: https://doi.org/10.20537/nd190206

Full text: PDF file (443 kB)
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MSC: 70E18, 70F40
Received: 12.04.2019
Accepted:28.05.2019

Citation: T. B. Ivanova, “The Rolling of a Homogeneous Ball with Slipping on a Horizontal Rotating Plane”, Nelin. Dinam., 15:2 (2019), 171–178

Citation in format AMSBIB
\Bibitem{Iva19}
\by T. B. Ivanova
\paper The Rolling of a Homogeneous Ball with Slipping on a Horizontal Rotating Plane
\jour Nelin. Dinam.
\yr 2019
\vol 15
\issue 2
\pages 171--178
\mathnet{http://mi.mathnet.ru/nd650}
\crossref{https://doi.org/10.20537/nd190206}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3983796}


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