Coupled metronomes on a moving platform with Coulomb friction.

Using a combination of theory, experiment, and simulation, we revisit the dynamics of two coupled metronomes on a moving platform. Our experiments show that the platform's motion is damped by a dry friction force of Coulomb type, not the viscous linear friction force that has often been assumed in the past. Prompted by this result, we develop a new mathematical model that builds on previously introduced models but departs from them in its treatment of friction on the platform.

Rethinking the definition of rate-induced tipping.

The current definition of rate-induced tipping is tied to the idea of a pullback attractor limiting in forward and backward time to a stable quasi-static equilibrium. Here, we propose a new definition that encompasses the standard definition in the literature for certain scalar systems and includes previously excluded N-dimensional systems that exhibit rate-dependent critical transitions.

Synchronization of clocks and metronomes: A perturbation analysis based on multiple timescales.

In 1665, Huygens observed that two pendulum clocks hanging from the same board became synchronized in antiphase after hundreds of swings. On the other hand, modern experiments with metronomes placed on a movable platform show that they often tend to synchronize in phase, not antiphase. Here, we study both in-phase and antiphase synchronization in a model of pendulum clocks and metronomes and analyze their long-term dynamics with the tools of perturbation theory.