Numerical simulation of non-central collisions of spherical magnets

TL;DR

This paper develops a computational model for simulating non-central collisions of spherical magnets, accurately capturing angular momentum conservation and rotational dynamics using detailed dipole-dipole interactions.

Contribution

It introduces a precise simulation method incorporating non-central dipole forces to model magnet collisions, improving upon simpler approximations.

Findings

Conservation of angular momentum confirmed in simulations.

Accurate prediction of final rotational frequencies.

Energy changes during collisions analyzed.

Abstract

We present a computational model of non-central collisions of two spherical neodymium-iron-boron magnets, suggested as a demonstration of angular momentum conservation. Our program uses an attractive dipole-dipole force and a repulsive contact force to solve the Newtonian equations of motion for the magnets. We confirm the conservation of angular momentum and study the changes in energy throughout the interaction. Using the exact expression for the dipole-dipole force, including non-central terms, we correctly model the final rotational frequencies, which is not possible with a simple power-law approximation.