Chaotic Dynamics of a Magnetic Pendulum

The magnetic pendulum is a simple system that can, depending on the setup, experience chaotic dynamics. Here, several permanent magnets are arranged below another, freely swinging, magnet that is attached via a rigid rod to its suspension above. All magnets are modeled as dipole moments with their respective dipole interaction [1]. The equations of motion can be derived within the Lagrangian formalism. The visualization on the right has been rendered using blender’s cycles engine. See for the bare animation. [1] J. Christian and H. Middleton-Spencer, “Chaos in the Magnetic Pendulum“, Math. Today 56, 70 (2020).