Group 5 2014

Members: Caligan, Lucas, Li, Norris

Introduction

In 1665, the Dutch scientist Christiaan Huygens discovered that two pendulum clocks mounted on the same wall synchronize with one another---the bobs swing with the same frequency but exactly out of phase, Huygen. The origin of this effect is weak coupling of the clocks mediated through the wall’s vibrations. Since then, the seemingly old topic of synchronization has developed into one of the most actively studied phenomena, in such diverse contexts as coupled lasers in optics, firing neurons in the brain, synchronous flashing by fireflies and rhythm of applause at concerts. It has been of conceptual interest to scientists in the fields of applied mathematics, nonlinear dynamics, statistical physics and material science.

Outline

The phenomena of synchronization in pendula lying along the same plane has been studied extensively in general. It was shown that several modes can occur in general. The possible configurations are complete synchronization of the system, synchronization of clusters of three or five pendula, or total antiphase synchronization. The paper Perlikowski claims that these phenomena can be observed in the laboratory. An extension of this would be to allow spherical pendula to synchronize along a plane instead of requiring the pendula to be along a straight line of the plane they lie on. This will allow higher dimensionality in the phase space and phenomena that may be observed. A further extension will be to allow the motion of the plane to be controlled by placing it on top of Meissner bodies. This will add more complexity to the system and hopefully more interesting dynamics as well.