TY - JOUR
T1 - An improved model for the classical Huygens' experiment on synchronization of pendulum clocks
AU - Pena Ramirez, J.
AU - Fey, R.H.B.
AU - Aihara, K.
AU - Nijmeijer, H.
PY - 2014
Y1 - 2014
N2 - 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'.
AB - 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'.
U2 - 10.1016/j.jsv.2014.08.030
DO - 10.1016/j.jsv.2014.08.030
M3 - Article
VL - 333
SP - 7248
EP - 7266
JO - Journal of Sound and Vibration
JF - Journal of Sound and Vibration
SN - 0022-460X
IS - 26
ER -