Tristability in the pendula chain

TL;DR

This paper demonstrates that a chain of coupled pendula can exhibit tristability and act as a frequency divider, with experimental, numerical, and analytical evidence revealing a novel odd-fraction output frequency regime.

Contribution

It introduces a new stationary state in pendula chains, modeled analytically, showing tristability and frequency division beyond traditional bistability understanding.

Findings

Experimental evidence of odd-fraction frequency output

Numerical simulations confirming the stationary state

Analytical model describing kink-like motion

Abstract

Experiments on a chain of coupled pendula driven periodically at one end demonstrate the existence of a novel regime which produces an output frequency at an odd fraction of the driving frequency. The new stationary state is then obtained on numerical simulations and modeled with an analytical solution of the continuous sine-Gordon equation that resembles a kink-like motion back and forth in the restricted geometry of the chain. This solution differs from the expressions used to understand nonlinear bistability where the synchronization constraint was the basic assumption. As a result the short pendula chain is shown to possess tristable stationary states and to act as a frequency divider.