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 Nelin. Dinam., 2016, Volume 12, Number 2, Pages 223–234 (Mi nd523)

Original papers

Pendulum system with an infinite number of equilibrium states and quasiperiodic dynamics

A. P. Kuznetsovab, S. P. Kuznetsovbac, Yu. V. Sedovaa

a Kotel’nikov’s Institute of Radio-Engineering and Electronics of RAS, Saratov Branch, ul. Zelenaya 38, Saratov, 410019 Russia
b Saratov State University, ul. Astrahanskaya 83, Saratov, 410012 Russia
c Udmurt State University, Universitetskaya 1, Izhevsk, 426034 Russia

Abstract: Examples of mechanical systems are discussed, where quasi-periodic motions may occur, caused by an irrational ratio of the radii of rotating elements that constitute the system. For the pendulum system with frictional transmission of rotation between the elements, in the conservative and dissipative cases we note the coexistence of an infinite number of stable fixed points, and in the case of the self-oscillating system the presence of many attractors in the form of limit cycles and of quasi-periodic rotational modes is observed. In the case of quasi-periodic dynamics the frequencies of spectral components depend on the parameters, but the ratio of basic incommensurate frequencies remains constant and is determined by the irrational number characterizing the relative size of the elements.

Keywords: dynamic system, mechanical transmission, quasi-periodic oscillations, attractor

 Funding Agency Grant Number Russian Science Foundation 15-12-20035 Russian Foundation for Basic Research 14-02-00085

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Document Type: Article
UDC: 517.9:531.36
MSC: 70E99, 37E99, 37C55, 37C70
Revised: 24.05.2016

Citation: A. P. Kuznetsov, S. P. Kuznetsov, Yu. V. Sedova, “Pendulum system with an infinite number of equilibrium states and quasiperiodic dynamics”, Nelin. Dinam., 12:2 (2016), 223–234

Citation in format AMSBIB
\Bibitem{KuzKuzSed16} \by A.~P.~Kuznetsov, S.~P.~Kuznetsov, Yu.~V.~Sedova \paper Pendulum system with an infinite number of equilibrium states and quasiperiodic dynamics \jour Nelin. Dinam. \yr 2016 \vol 12 \issue 2 \pages 223--234 \mathnet{http://mi.mathnet.ru/nd523} \elib{http://elibrary.ru/item.asp?id=26193559} 

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This publication is cited in the following articles:
1. 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
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