Synchronizing Huygens's clocks
Rui Dilao

TL;DR
This paper presents a new interaction mechanism for oscillators that achieves exact in-phase and anti-phase synchronization, explaining the synchronization observed in Huygens's pendulum clocks and showing how coupling alters oscillation periods.
Contribution
It introduces a novel coupling mechanism for nonlinear oscillators that accounts for synchronization phenomena seen in historical experiments.
Findings
Achieves exact in-phase and anti-phase synchronization
Explains Huygens's pendulum clocks synchronization
Shows period change due to coupling
Abstract
We introduce an interaction mechanism between oscillators leading to exact anti-phase and in-phase synchronization. This mechanism is applied to the coupling between two nonlinear oscillators with a limit cycle in phase space, leading to a simple justification of the anti-phase synchronization observed in the Huygens's pendulum clocks experiment. If the two coupled nonlinear oscillators reach the anti-phase or the in-phase synchronized oscillatory state, the period of oscillation is different from the eigen-periods of the uncoupled oscillators.
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Taxonomy
TopicsScientific Research and Discoveries · Quantum chaos and dynamical systems · Astro and Planetary Science
