Synchronizing Huygens's clocks

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.