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Nelin. Dinam., 2015, Volume 11, Number 4, Pages 709–720 (Mi nd503)  

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

Original papers

A modified model of coupled pendulums

M. A. Guzev, A. A. Dmitriev

Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, Radio 7, Vladivostok, 690041, Russia

Abstract: We consider a modified system of two pendulums rods of which intersect and slide without any friction. The pendulums are connected by an elastic linear spring and arranged in a fixed vertical plane of the uniform gravity field. We have shown that there are symmetric and asymmetric equilibrium solutions with respect to the vertical axis. It is revealed that the stability of the model depends on two parameters, the first one specifies the spring stiffness, and the second one defines the distance between the hinges. The conditions of stability and instability of the symmetric equilibrium are obtained in the upper and lower position of pendulums. The analysis of asymmetric equilibrium solutions and stability conditions is carried out for long pendulums. Comparison with the sympathetic pendulums model proposed by Sommerfeld indicates that asymmetric solutions exist only for the modified model.

Keywords: pendulum, equilibrium, stability

Funding Agency Grant Number
Russian Science Foundation 14-11-00079


Full text: PDF file (545 kB)
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Document Type: Article
UDC: 531.36, 531.53
MSC: 70E55, 70H12, 70H14
Received: 13.04.2015
Revised: 10.10.2015

Citation: M. A. Guzev, A. A. Dmitriev, “A modified model of coupled pendulums”, Nelin. Dinam., 11:4 (2015), 709–720

Citation in format AMSBIB
\Bibitem{GuzDmi15}
\by M.~A.~Guzev, A.~A.~Dmitriev
\paper A modified model of coupled pendulums
\jour Nelin. Dinam.
\yr 2015
\vol 11
\issue 4
\pages 709--720
\mathnet{http://mi.mathnet.ru/nd503}


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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. A. P. Evdokimenko, “On equilibrium configurations and their stability for a system of two coupled pendulums”, Mech. Sol., 52:3 (2017), 266–277  crossref  isi  scopus
  • Нелинейная динамика
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