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Dal'nevost. Mat. Zh., 2015, Volume 15, Number 2, Pages 166–191 (Mi dvmg307)  

Stability of coupled oscillators

M. A. Guzev, A. A. Dmitriev

Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, Vladivostok

Abstract: We study a system of two coupled oscillators and a modified system of these oscillators whose rods intersect and slide without friction relative to each other. The oscillators posed vertically in a uniform gravity field and its interaction is described by a potential depending on distance. We demonstrate that both systems have symmetrical and asymmetrical equilibrium states. Stability of the states depend on the interaction energy and distance between the oscillators' suspension centers. Stability regions for Hooke and Coulomb potentials are calculated in the parameter plane.

Key words: coupled oscillators, equilibrium, stability

Full text: PDF file (463 kB)
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UDC: 531.36, 531.53
MSC: Primary 70E55; Secondary 70H12, 70H14
Received: 26.10.2015

Citation: M. A. Guzev, A. A. Dmitriev, “Stability of coupled oscillators”, Dal'nevost. Mat. Zh., 15:2 (2015), 166–191

Citation in format AMSBIB
\Bibitem{GuzDmi15}
\by M.~A.~Guzev, A.~A.~Dmitriev
\paper Stability of coupled oscillators
\jour Dal'nevost. Mat. Zh.
\yr 2015
\vol 15
\issue 2
\pages 166--191
\mathnet{http://mi.mathnet.ru/dvmg307}
\elib{http://elibrary.ru/item.asp?id=25058092}


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