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Nelin. Dinam., 2013, Volume 9, Number 1, Pages 27–38 (Mi nd367)  

This article is cited in 6 scientific papers (total in 6 papers)

A motion of connected pendulums

Anatoly P. Markeev

A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia

Abstract: A motion of two identical pendulums connected by a linear elastic spring with an arbitrary stiffness is investigated. The system moves in an homogeneous gravitational field in a fixed vertical plane. The paper mainly studies the linear orbital stability of a periodic motion for which the pendulums accomplish identical oscillations with an arbitrary amplitude. This is one of two types of nonlinear normal oscillations. Perturbational equations depend on two parameters, the first one specifies the spring stiffness, and the second one defines the oscillation amplitude. Domains of stability and instability in a plane of these parameters are obtained.
Previously [1, 2] the problem of arbitrary linear and nonlinear oscillations of a small amplitude in a case of a small spring stiffness was investigated.

Keywords: pendulum, nonlinear oscillation, stability.

Full text: PDF file (371 kB)
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UDC: 531.36,531.53
MSC: 70E55,70H12,70H14
Received: 23.01.2013
Revised: 01.03.2012

Citation: Anatoly P. Markeev, “A motion of connected pendulums”, Nelin. Dinam., 9:1 (2013), 27–38

Citation in format AMSBIB
\Bibitem{Mar13}
\by Anatoly~P.~Markeev
\paper A motion of connected pendulums
\jour Nelin. Dinam.
\yr 2013
\vol 9
\issue 1
\pages 27--38
\mathnet{http://mi.mathnet.ru/nd367}


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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. A. P. Markeev, “Uproschenie struktury form tretei i chetvertoi stepenei v razlozhenii funktsii Gamiltona pri pomoschi lineinogo preobrazovaniya”, Nelineinaya dinam., 10:4 (2014), 447–464  mathnet
    2. M. A. Guzev, A. A. Dmitriev, “Stabilnost svyazannykh mayatnikov”, Dalnevost. matem. zhurn., 15:2 (2015), 166–191  mathnet  elib
    3. M. A. Guzev, A. A. Dmitriev, “Modifitsirovannaya model svyazannykh mayatnikov”, Nelineinaya dinam., 11:4 (2015), 709–720  mathnet
    4. Lev A. Smirnov, Alexey K. Kryukov, Grigory V. Osipov, Jürgen Kurths, “Bistability of Rotational Modes in a System of Coupled Pendulums”, Regul. Chaotic Dyn., 21:7-8 (2016), 849–861  mathnet  crossref
    5. M. A. Kovaleva, V. V. Smirnov, L. I. Manevich, “Statsionarnaya i nestatsionarnaya dinamika sistemy dvukh garmonicheski svyazannykh mayatnikov”, Nelineinaya dinam., 13:1 (2017), 105–115  mathnet  crossref  elib
    6. V. M. Budanov, “Metod neopredelennykh chastot”, Fundament. i prikl. matem., 22:2 (2018), 59–71  mathnet
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