Related papers: Huygens synchronization of two pendulum clocks
In 1665, Christiaan Huygens reported the observation of the synchronization of two pendulum clocks hanged on the wall of his workshop. After synchronization, the clocks swung exactly in the same frequency and $180^{o}$ out of phase --…
In 1665, Huygens observed that two pendulum clocks hanging from the same board became synchronized in antiphase after hundreds of swings. On the other hand, modern experiments with metronomes placed on a movable platform show that they…
We introduce an interaction mechanism between oscillators leading to exact anti-phase and in-phase synchronization. This mechanism is applied to the coupling between two nonlinear oscillators with a limit cycle in phase space, leading to a…
We study two models of connected pendulum clocks synchronizing their oscillations, a phenomenon originally observed by Huygens. The oscillation angles are assumed to be small so that the pendulums are modeled by harmonic oscillators, clock…
This paper investigates the synchronization of three identical oscillators, or clocks, suspended from a common rigid support. We consider scenarios where each clock interacts with the other two, achieving synchronization through small…
This study examines the synchronization of three identical oscillators arranged in an array and coupled by small impacts, wherein each oscillator interacts solely with its nearest neighbor. The synchronized state, which is asymptotically…
353 years ago, in a letter to the Royal Society of London, 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 in coupled…
The phenomenon of phase synchronization was evidenced in the 17th century by Huygens while observing two pendulums of clocks leaning against the same wall. This phenomenon has more recently appeared as a widespread phenomenon in nature, and…
Weakly coupled oscillators adjust their dynamics to work in unison: they synchronize. This ubiquitous phenomenon is observed for oscillating pendulum, electronic devices, as well as clapping crowds or flashing fireflies. In effect,…
The model we consider consists in a double pendulum set, where the pivot points are free to shift along a horizontal line. Moreover, the two pendula are coupled by means of a spring whose extremities connect two points of each pendulum, at…
We propose a quantum analogue of the Huygens clock, in which the phases of two spins achieve synchronization through their interaction with a shared environment. The environment functions analogously to the escapement mechanism in a…
We present an algorithm for synchronizing two clocks based on second-order quantum interference between entangled photons generated by parametric down-conversion. The procedure is distinct from the standard Einstein two-way clock…
The synchronization between two dynamical systems is one of the most appealing phenomena occurring in Nature. Already observed by Huygens in the case of two pendula, it is a current area of research in the case of chaotic systems, with…
While Einstein clocks synchronization process is performed, one has a well defined region in which the clocks are synchronized and another one in which the clocks are not yet synchronized. The frontier between them evolves differently from…
Lyapunov functions are essential tools in dynamical systems, as they allow the stability analysis of equilibrium points without the need to explicitly solve the system's equations. Despite their importance, no systematic method exists for…
This paper investigates the dynamical system governing the phase differences between three identical oscillators arranged symmetrically and coupled by burst interactions. By constructing a discrete Lyapunov function, we prove the existence…
This article provides a self-contained comprehensive review of the phenomenon of synchronization in dynamical systems, with a particular focus on chaotic systems in both continuous-time and discrete-time contexts. Synchronization, initially…
We consider the synchronization of two self-excited double pendula. We show that such pendula hanging on the same beam can have four different synchronous configurations. Our approximate analytical analysis allows us to derive the…
We numerically study the synchronization of two nonidentical pendulum motions, pivoting on a common movable frame in the point of view of the dynamic phase transition. When the difference in the pendulum lengths is not too large, it is…
Galileo noted in the 16th century that the period of oscillation of a pendulum is almost independent of the amplitude. However, such a pendulum is damped by air friction. The latter may be viewed as resulting from air molecules getting in…