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


Cite this article as:

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

Language: 
Russian

Rotational dynamics in the system of two coupled pendulums

Autors: 
Smirnov Lev Aleksandrovich, Institute of Applied Physics of the Russian Academy of Sciences
Krjukov Aleksej Konstantinovich, Federal state budgetary educational institution of higher professional education "Nizhny Novgorod state University named N. And.Lobachevsky"
Osipov Grigorij Vladimirovich, Federal state budgetary educational institution of higher professional education "Nizhny Novgorod state University named N. And.Lobachevsky"
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.   Download full version

DOI: 
10.18500/0869-6632-2015-23-5-41-61
References: 

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