ROTATIONAL DYNAMICS IN THE SYSTEM OF TWO COUPLED PENDULUMS
Cite this article as:
Smirnov L. А., Kryukov А. К., 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: https://doi.org/10.18500/0869-6632-2015-23-5-41-61
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.
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BibTeX
author = {L. А. Smirnov and А. К. Kryukov and G. V. Osipov },
title = {ROTATIONAL DYNAMICS IN THE SYSTEM OF TWO COUPLED PENDULUMS},
year = {2015},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {23},number = {5},
url = {https://old-andjournal.sgu.ru/en/articles/rotational-dynamics-in-the-system-of-two-coupled-pendulums},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2015-23-5-41-61},pages = {41--61},issn = {0869-6632},
keywords = {synchronization,oscillator,nonlinear dynamics},
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 }}