Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
in January 1966
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IssuesArchive of Issues2016-4pp.395-405

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Total articles in the database: 9179
In Russian (. . ): 6485
In English (Mech. Solids): 2694

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A.A. Burov and E.S. Shalimova, "Bifurcations of Relative Equilibria of a Heavy Bead on a Rotating Parabolic Bowl with Dry Friction," Mech. Solids. 51 (4), 395-405 (2016)
Year 2016 Volume 51 Number 4 Pages 395-405
DOI 10.3103/S0025654416040038
Title Bifurcations of Relative Equilibria of a Heavy Bead on a Rotating Parabolic Bowl with Dry Friction
Author(s) A.A. Burov (Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333 Russia; National Research University "Higher School of Economics," ul. Myasnitskaya 20, Moscow, 101000 Russia,
E.S. Shalimova (Lomonosov Moscow State University, Moscow, 119992 Russia,
Abstract The motion of a heavy bead on the surface of a parabolic bowl rotating at a constant angular velocity about its axis, which coincides with the vertical, is considered. It is assumed that the dry friction force acts between the bead and the bowl. The sets of nonisolated relative equilibria of the bead on the bowl are determined, and their dependence on the problem parameters is studied. The results are illustrated in the form of bifurcation diagrams.
Keywords systems with friction, relative equilibria, dry friction
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8.  R. I. Leine, "Bifurcations of Equilibria in Non-Smooth Continuous Systems," Physica D 223, 121-137 (2006).
9.  A. Teufel, A. Steindl, and H. Troger, "Classification of Nonsmooth Bifurcations for Oscillator with Friction," in Problems of Analytic Mechanics and Stability, Collection of scientific papers dedicated to the memory of Academician V. V. Rumyantsev (IPM RAS, Moscow, 2009), pp. 161-175 [in Russian].
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12.  A. A. Burov, "On Bifurcations of Relative Equilibria of a Heavy Bead Sliding with Dry Friction on a Rotating Circle," Acta Mech. 212 (3-4), 349-354 (2010).
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14.  A. A. Burov and I. A. Yakushev, "Bifurcations of the Relative Equilibria of a Heavy Bead on a Rotating Hoop with Dry Friction," Prikl. Mat. Mekh. 78 (5), 645-655 (2014) [J. Appl. Math. Mech. (Engl. Transl.) 78 (5), 460-467 (2014)].
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19.  A. A. Burov, "Small Sigma and Problems with Moduli," Kvant, No. 1, 36-38 (2012).
Received 10 December 2014
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