Vol. 4, No. 2, 2016

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ISSN: 2325-3444 (e-only)
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Stability analysis of two coupled oscillators

Mickhail A. Guzev and Alexandr A. Dmitriev

Vol. 4 (2016), No. 2, 139–152
DOI: 10.2140/memocs.2016.4.139
Abstract

We study a system of two coupled oscillators linked by a linear elastic spring and positioned vertically in a uniform gravity field. It is demonstrated that the system has different equilibrium configurations below and above the oscillators’ suspension centers. We obtained the relations of the string stiffness and the distance between the suspension centers identifying the stability region of the oscillators.

Keywords
coupled oscillators, equilibrium configurations, stability, linear interaction
Mathematical Subject Classification 2010
Primary: 70E55, 70H14
Milestones
Received: 8 November 2015
Revised: 11 April 2016
Accepted: 14 May 2016
Published: 21 November 2016

Communicated by Francesco dell'Isola
Authors
Mickhail A. Guzev
Institute for Applied Mathematics
Far Eastern Branch
Russian Academy of Sciences
Radio 7
Vladivostok
690041
Russia
Alexandr A. Dmitriev
Institute for Applied Mathematics
Far Eastern Branch
Russian Academy of Sciences
Radio 7
Vladivostok
690041
Russia