From harmonic oscillation to chaotic motion of a compass

Abstract

With secondary school students at the age of 17-20 years old, we described compass motion in uniform-immobile, uniform rotating and their superposed magnetic fields. As the students have already known the kinematics, dynamics and energy analysis of a simple pendulum in harmonic case, we tried to find analogies between pendulum and compass. Using Dynamic Solver freeware software and two representation types, phase-plane and stroboscopic projection, we simulated and analysed compass motions in more and more complex cases. Finally, we searched chaotic attractors, the sign of chaotic motion, on stroboscopic projections. A new type of representation, a video where every picture is a stroboscopic projection, helped to understand our results. This study was funded by the Content Pedagogy Research Program of the Hungarian Academy of Sciences.