An improved model for the classical Huygens' experiment on synchronization of pendulum clocks

This paper introduces a new model for the classical Huygens' experiment on synchronization of two pendulum clocks hanging from a wooden coupling structure. The dynamics of the coupling - a beam with supporting structure - is modelled in detail using the Finite Element method. The pendula are considered as single dof systems, i.e. local nonlinearities including the escapement. Consequently, the resulting coupled model consists of a finite set of nonlinear ordinary differential equations. Then, the existence of synchronous motion in the system is analytically investigated. Furthermore, this model is used in order to obtain numerical results illustrating the possible limit behaviour of the system. Besides in-phase and anti-phase synchronization, other kinds of limit behaviour appear, namely quenching, beating death, and modulating behaviour, phenomena, which `Huygens did not see'.