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Mathematics and Mechanics

Russian Academy of Sciences
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in January 1936
(Translated from 1958)
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ISSN 0021-8928
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IssuesArchive of Issues2014-5pp.460-467

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A.A. Burov and I.A. Yakushev, "Bifurcations of the relative equilibria of a heavy bead on a rotating hoop with dry friction," J. Appl. Math. Mech. 78 (5), 460-467 (2014)
Year 2014 Volume 78 Issue 5 Pages 460-467
Title Bifurcations of the relative equilibria of a heavy bead on a rotating hoop with dry friction
Author(s) A.A. Burov (Moscow, Russia)
I.A. Yakushev (Moscow, Russia, jtm@ya.ru)
Abstract The sliding of a heavy bead, threaded on a thin circular hoop, rotating with a constant angular velocity around a vertical axis, situated in its plane and, in the general case, not passing through its vertical diameter, is considered. It is assumed that dry friction acts between the bead and the hoop. A set of unisolated positions of relative equilibrium of the bead on the hoop is obtained, and their dependence on the problem parameters is investigated. The results are presented in the form of bifurcation diagrams. The stability properties of the unisolated relative equilibria obtained are discussed.
Received 23 January 2014
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