Huygens’ synchronization experiment revisited: luck or skill?

Abstract

In a letter to the Royal Society of London in February of 1665, Christiaan Huygens described ‘an odd kind of sympathy’ between two pendulums mounted side by side on a wooden beam, which inspired the modern studies of synchronization of coupled nonlinear oscillators. Despite the growth of synchronization studies in a variety of disciplines, the original phenomenon described by Huygens remains a puzzle to researchers. Here, by placing two mechanical metronomes on top of a freely moving plastic board, we revisit the synchronization experiment conducted by Huygens. Experimental results show that by introducing a small mismatch to the natural frequencies of the metronomes, the probability of generating the anti-phase synchronization (APS) state, i.e. the ‘odd sympathy’ described by Huygens, can clearly be increased. By numerical simulations of the system dynamics, we conduct a detailed analysis of the influence of frequency mismatch on APS. It is found that as the frequency mismatch increases from zero, the attracting basin of the APS is gradually enlarged and, in the meantime, the basin of the in-phase synchronization (IPS) is reduced. However, as the frequency mismatch exceeds some critical value, both the basins of APS and IPS suddenly disappear, resulting in the desynchronization states. The impacts of the friction coefficient and synchronization precision on APS are also studied, and it is found that with the increase of the friction coefficient and the precision requirement of APS, the critical frequency mismatch for desynchronization will decrease. Our study indicates that, instead of luck, Huygens might have introduced, deliberately and elaborately, a small frequency mismatch to the pendulums in his experiment for generating the odd sympathy.