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IssuesArchive of Issues2004-5pp.11-16

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I. G. Boruk, L. G. Lobas, and L. D. Patricio, "Equilibrium states of an inverted pendulum acted upon by a follower force on the elastically restrained upper end," Mech. Solids. 39 (5), 11-16 (2004)
Year 2004 Volume 39 Number 5 Pages 11-16
Title Equilibrium states of an inverted pendulum acted upon by a follower force on the elastically restrained upper end
Author(s) I. G. Boruk (Kiev, Covilia (Portugal))
L. G. Lobas (Kiev, Covilia (Portugal))
L. D. Patricio (Kiev, Covilia (Portugal))
Abstract A model of an elastic beam subjected to a follower force represented by an inverted two-link pendulum with elastoviscous joints is studied. It is shown that a divergent bifurcation can occur at certain values of the magnitude of the follower force and stiffness of the elastic restraint. As a result of this bifurcation, the vertical equilibrium becomes unstable and two new non-vertical equilibrium states appear. This bifurcation is referred to as the fork bifurcation or triple equilibrium bifurcation.
References
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3.  Ya. G. Panovko and S. V. Sorokin, Quasi-stability of elastoviscous systems with follower forces," Izv. AN SSSR. MTT [Mechanics of Solids], No. 5, pp. 135-139, 1970.
4.  H. Troger and A. Steindl, Nonlinear Stability and Bifurcation Theory, Springer, Wien, New York, 1991.
5.  S. A. Agafonov, "Stability and self-sustained vibrations of a double pendulum with elastic members under the action of a follower force," Izv. AN. MTT [Mechanics of Solids], No. 5, pp. 185-190, 1992.
6.  S. A. Agafonov, "Stabilization of the equilibrium of Ziegler's pendulum by means of parametric excitation," Izv. AN. MTT [Mechanics of Solids], No. 6, pp. 36-40, 1997.
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8.  A. P. Seiranyan, "Stabilization of non-conservative systems by dissipative forces and indeterminacy of the critical load," Doklady RAN, Vol. 348, No. 3, pp. 323-326, 1996.
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10.  L. G. Lobas, "Nonlinear stability and fork-type bifurcations in dynamical systems with the simplest symmetry," PMM [Applied Mathematics and Mechanics], Vol. 60, No. 2, pp. 327-332, 1996.
11.  A. M. Lyapunov, Collected Works. Volume 2 [in Russian], Izd-vo AN SSSR, Moscow, Leningrad, 1956.
12.  V. G. Verbitskii and L. G. Lobas, "Real bifurcations in two-link systems with rolling," PMM [Applied Mathematics and Mechanics], Vol. 60, No. 3, pp. 418-425, 1996.
Received 21 January 2002
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