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Regul. Chaotic Dyn., 2015, Volume 20, Issue 3, Pages 225–233 (Mi rcd30)  

This article is cited in 2 scientific papers (total in 2 papers)

On the Motion of a Heavy Material Point on a Rotating Sphere (Dry Friction Case)

Alexander A. Burovab, Ekaterina S. Shalimovac

a Dorodnicyn Computing center of the RAS, ul. Vavilova 40, Moscow
b Higher School of Economics, ul. Myasnitskaya 20, Moscow, 101000 Russia
c Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119991 Russia

Abstract: The problem of motion of a heavy particle on a sphere uniformly rotating about a fixed axis is considered in the case of dry friction. It is assumed that the angle of inclination of the rotation axis is constant. The existence of equilibria in an absolute coordinate system and their linear stability are discussed. The equilibria in a relative coordinate system rotating with the sphere are also studied. These equilibria are generally nonisolated. The dependence of the equilibrium sets of this kind on the system parameters is also considered.

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

DOI: https://doi.org/10.1134/S1560354715030028

References: PDF file   HTML file

Bibliographic databases:

MSC: 70F40, 70K42, 70K50
Received: 10.01.2015
Language:

Citation: Alexander A. Burov, Ekaterina S. Shalimova, “On the Motion of a Heavy Material Point on a Rotating Sphere (Dry Friction Case)”, Regul. Chaotic Dyn., 20:3 (2015), 225–233

Citation in format AMSBIB
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\by Alexander A. Burov, Ekaterina S. Shalimova
\paper On the Motion of a Heavy Material Point on a Rotating Sphere (Dry Friction Case)
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 3
\pages 225--233
\mathnet{http://mi.mathnet.ru/rcd30}
\crossref{https://doi.org/10.1134/S1560354715030028}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84935009304}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. S. Shalimova, “O dvizhenii tyazheloi tochki po sfere, vraschayuscheisya vokrug ne prokhodyaschei cherez ee tsentr vertikalnoi osi, pri nalichii sukhogo treniya”, Nelineinaya dinam., 12:3 (2016), 369–383  mathnet  crossref  mathscinet  elib
    2. A. A. Burov, I. I. Kosenko, E. S. Shalimova, “Relative equilibria of a massive point on a uniformly rotating asteroid”, Dokl. Phys., 62:7 (2017), 359–362  crossref  mathscinet  isi  scopus
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