Abstract
It is considered collective dynamics of two non-linearly coupled pendulums in the presence of dissipation and constant external torque applied to each element. It has in-phase periodic rotation in addition to stable steady state. Numerical experiments demonstrate that the in-phase motion becomes unstable at certain coupling strength values. It is proposed an asymptotic theory which provides explanation of in-phase motion instability at the limit of low dissipation. Analytic equations for the bifurcation coupling values are found. Numerical modeling also indicates that there is a coupling strength range characterized by existence of a pair (stable and unstable) non in-phase rotation cycles. In other words, we demonstrate periodical motions bi-stability in a pair of non-linearly coupled pendulums. It is also investigated bifurcations corresponding to non in-phase rotation motions origination and dissolution. Keywords: pendulum, collective dynamics, in-phase regime, parametric instability.
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