ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Smirnov L. A., Kryukov A. K., Osipov G. V. Rotational dynamics in the system of two coupled pendulums. Izvestiya VUZ. Applied Nonlinear Dynamics, 2015, vol. 23, iss. 5, pp. 41-61. DOI: 10.18500/0869-6632-2015-23-5-41-61

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Language: 
Russian
Heading: 
Applied Problems of Nonlinear Oscillation and Wave Theory
Article type: 
Article
UDC: 
621.391.01
DOI: 
10.18500/0869-6632-2015-23-5-41-61

Rotational dynamics in the system of two coupled pendulums

Autors: 
Smirnov Lev Aleksandrovich, Institute of Applied Physics of the Russian Academy of Sciences
Kryukov Aleksej Konstantinovich, Lobachevsky State University of Nizhny Novgorod
Osipov Grigorij Vladimirovich, Lobachevsky State University of Nizhny Novgorod
Abstract: 

We consider dynamics in a pair of nonlinearly coupled pendulums. With existence of dissipation and constant torque such system can demonstrate in-phase periodical rotation in addition to the stable state. We have shown in numerical simulations that such in- phase rotation becomes unstable at certain values of coupling strength. In the limit of small dissipation we have created an asymptotic theory that explains instability of the in-phase cycle. Found analytical equations for coupling strength values corresponding to the boundaries of the instability area. Numerical simulations show that there is a coupling strength interval where the system can have a pair of stable and unstable non in-phase cycles in addition to the stable in-phase motion. Therefore, we demonstrated that nonlinearly coupled pendulums have a bi-stability of the limit cycles. Analysed bifurcations which lead to originating and disappearing of non in-phase cycles.

Key words: 
synchronization
oscillator
nonlinear dynamics
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Received: 
19.11.2015
Accepted: 
15.12.2015
Published: 
29.04.2016
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