Chaos in undamped, forced oscillators via stroboscopic maps

TL;DR

This paper demonstrates how chaos can be visualized in simple, forced oscillators using stroboscopic maps, making the complex topic accessible in introductory physics courses without extensive chaos theory background.

Contribution

It introduces a practical method to include chaos visualization in basic classical mechanics courses through stroboscopic maps of non-linear oscillators.

Findings

Chaos appears in forced oscillators as shown by stroboscopic maps.

The method applies to simple pendulums and other conservative systems.

It provides an accessible way to introduce chaos in undergraduate physics.

Abstract

Non-linear dynamics is not a usually covered topic in undergraduate physics courses. However, its importance within classical mechanics and the general theory of dynamical systems is unquestionable. In this work we show that this subject can be included in the schedule of an introductory classical mechanics course without the need to develop a robust theory of chaotic dynamics. To do this, we take as examples conservative non-linear oscillators subject to time-dependent periodic forces. By introducing the concept of stroboscopic maps we show that it is possible to visualize the appearance of chaos in these systems. We also address the example of the forced simple pendulum applying the same treatment. Finally, we briefly comment on the more general theory of chaos in conservative Hamiltonian systems.