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Nelin. Dinam., 2010, Volume 6, Number 1, Pages 79–89 (Mi nd57)  

This article is cited in 2 scientific papers (total in 2 papers)

On periodic perturbations of self-oscillating pendulum equations

S. A. Korolev, A. D. Morozov.

N. I. Lobachevski State University of Nizhni Novgorod

Abstract: In this paper we consider time-periodic perturbations of self-oscillating pendulum equation which arises from analysis of one system with two degrees of freedom. We derive averaged systems which describe the behavior of solutions of original equation in resonant areas and we find existence condition of Poincar homoclinic structure. In the case when autonomous equation has 5 limit cycles in oscillating region we give results of numerical computation. Under variation of perturbation frequency we investigate bifurcations of phase portraits of Poincar map.

Keywords: pendulum equation, limit cycles, resonances.

Full text: PDF file (782 kB)
References: PDF file   HTML file
UDC: 517.9, 534.1
MSC: 34C15, 79K30
Received: 05.10.2009

Citation: S. A. Korolev, A. D. Morozov., “On periodic perturbations of self-oscillating pendulum equations”, Nelin. Dinam., 6:1 (2010), 79–89

Citation in format AMSBIB
\Bibitem{KorMor10}
\by S.~A.~Korolev, A.~D.~Morozov.
\paper On periodic perturbations of self-oscillating pendulum equations
\jour Nelin. Dinam.
\yr 2010
\vol 6
\issue 1
\pages 79--89
\mathnet{http://mi.mathnet.ru/nd57}
\elib{http://elibrary.ru/item.asp?id=13411470}


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    This publication is cited in the following articles:
    1. Korolev S.A., “O rezonansakh v sisteme dvukh slabosvyazannykh mayatnikov”, Vestn. Nizhegorodskogo un-ta im. N. I. Lobachevskogo, 2010, no. 5-1, 149–157  elib
    2. L. A. Klimina, B. Ya. Lokshin, “Ob odnom konstruktivnom metode poiska rotatsionnykh i avtokolebatelnykh rezhimov v avtonomnykh dinamicheskikh sistemakh”, Nelineinaya dinam., 13:1 (2017), 25–40  mathnet  crossref  elib
  • Нелинейная динамика
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