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Nelin. Dinam., 2015, Volume 11, Number 4, Pages 685–707 (Mi nd502)  

This article is cited in 1 scientific paper (total in 1 paper)

Original papers

On stability of permanent rotation of a disk that collides with an horizontal plane

A. P. Markeev

A.Ishlinsky Institite for Problems in M echanics, Russian Academy of Sciences, pr. Vernadskogo 101-1, Moscow, 119526, Russia

Abstract: Stability of the motion of a thin homogeneous disk in a uniform gravitational field above a fixed horizontal plane is investigated. Collisions between the disk and the plane are assumed to be absolutely elastic, and friction is negligible. In unperturbed motion, the disk rotates at a constant angular velocity about its vertical diameter, and its center of gravity makes periodic oscillations along a fixed vertical as a result of collisions. The stability problem depends on two dimensionless parameters characterizing the magnitude of the angular velocity of the disk and the height of his jump above the plane in the unperturbed motion. An exact solution of the problem of stability is obtained for all physically admissible values of these parameters.

Keywords: stability, map, canonical transformations

Funding Agency Grant Number
Russian Foundation for Basic Research 14.01.00380
Ministry of Education and Science of the Russian Federation НШ-2363.2014.1


Full text: PDF file (459 kB)
References: PDF file   HTML file
UDC: 531.38
MSC: 70H05, 70H15, 70E50
Received: 13.10.2015
Revised: 05.11.2015

Citation: A. P. Markeev, “On stability of permanent rotation of a disk that collides with an horizontal plane”, Nelin. Dinam., 11:4 (2015), 685–707

Citation in format AMSBIB
\Bibitem{Mar15}
\by A.~P.~Markeev
\paper On stability of permanent rotation of a disk that collides with an horizontal plane
\jour Nelin. Dinam.
\yr 2015
\vol 11
\issue 4
\pages 685--707
\mathnet{http://mi.mathnet.ru/nd502}


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  • http://mi.mathnet.ru/eng/nd/v11/i4/p685

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. T. E. Churkina, “The stability of the rotation of a spheroid about a horizontal axis with impacts on a horizontal plane”, J. Appl. Math. Mech., 80:4 (2016), 290–301  crossref  isi
  • Нелинейная динамика
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