Geodesic
Rotational dynamics in the system of two coupled pendulums
Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 23 (2015) no. 5, pp. 41-61.

Voir la notice de l'article provenant de la source Math-Net.Ru

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 inphase 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.
Keywords: Synchronization, oscillator, nonlinear dynamics. 
@article{IVP_2015_23_5_a2,
     author = {L. A. Smirnov and A. K. Kryukov and G. V. Osipov},
     title = {Rotational dynamics in the system of two coupled pendulums},
     journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
     pages = {41--61},
     publisher = {mathdoc},
     volume = {23},
     number = {5},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVP_2015_23_5_a2/}
}
TY  - JOUR
AU  - L. A. Smirnov
AU  - A. K. Kryukov
AU  - G. V. Osipov
TI  - Rotational dynamics in the system of two coupled pendulums
JO  - Izvestiya VUZ. Applied Nonlinear Dynamics
PY  - 2015
SP  - 41
EP  - 61
VL  - 23
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVP_2015_23_5_a2/
LA  - ru
ID  - IVP_2015_23_5_a2
ER  - 
%0 Journal Article
%A L. A. Smirnov
%A A. K. Kryukov
%A G. V. Osipov
%T Rotational dynamics in the system of two coupled pendulums
%J Izvestiya VUZ. Applied Nonlinear Dynamics
%D 2015
%P 41-61
%V 23
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVP_2015_23_5_a2/
%G ru
%F IVP_2015_23_5_a2
L. A. Smirnov; A. K. Kryukov; G. V. Osipov. Rotational dynamics in the system of two coupled pendulums. Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 23 (2015) no. 5, pp. 41-61. http://geodesic.mathdoc.fr/item/IVP_2015_23_5_a2/