Clustering of huygens' clocks

Abstract

We study synchronization of a number of pendulum clocks hanging from an elastically fixed horizontal beam. It has been shown that after a transient, different types of synchronization between pendulums can be observed; (i) the complete synchronization in which all pendulums behave identically, (ii) pendulums create three or five clusters of synchronized pendulums, (iii) anti-phase synchronization in pairs (for even n). We give evidence why the configurations with a different number of clusters are not observed.