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Nelin. Dinam., 2016, Volume 12, Number 3, Pages 369–383 (Mi nd533)  

Original papers

On the motion of a material point on a rotating sphere with dry friction (the case of the vertical axis)

E. S. Shalimova

Research Institute of Mechanics, Lomonosov Moscow State University, Michurinsky pr. 1, Moscow, Russia, 119192

Abstract: The motion of a heavy point on the surface of a rotating sphere is considered. It is assumed that the rotation axis does not coincide with the vertical diameter of the sphere and the angular velocity of the sphere is constant. The Lagrange equations for this system are derived. Sets of relative equilibria are found and their dependence on the parameters of the system is studied in extreme cases when the magnitude of the angular velocity or the distance between the rotation axis and the center of the sphere is large. The results are represented in graphic form. The same graphic series are also numerically plotted in the general case.

Keywords: motion of a particle on a sphere, dry friction, relative equilibria

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00625 а


DOI: https://doi.org/10.20537/nd1603006

Full text: PDF file (542 kB)
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Bibliographic databases:

Document Type: Article
UDC: 531.36
MSC: 70F40
Received: 27.12.2015

Citation: E. S. Shalimova, “On the motion of a material point on a rotating sphere with dry friction (the case of the vertical axis)”, Nelin. Dinam., 12:3 (2016), 369–383

Citation in format AMSBIB
\Bibitem{Sha16}
\by E.~S.~Shalimova
\paper On the motion of a material point on a rotating sphere with dry friction (the case of the vertical axis)
\jour Nelin. Dinam.
\yr 2016
\vol 12
\issue 3
\pages 369--383
\mathnet{http://mi.mathnet.ru/nd533}
\crossref{https://doi.org/10.20537/nd1603006}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1834792}
\elib{http://elibrary.ru/item.asp?id=27328720}


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