Periodic Solutions to Two Magnetic Sphere Interactions

The purpose of this research project is to solve the equations of motion for two
uniformly magnetized spheres, one of which is fixed, the other of which is free to move about.
We will look to find what sort of periodic motion the free magnet exhibits as it bounces
around the fixed sphere, with energy conserved. Previous research has
shown that the magnetic energy, forces, and torques of two uniformly magnetized spheres
are identical to the interactions of point magnetic dipoles. There was additional research
done into finding periodic nonlinear sliding modes for these spheres and their dynamical
interactions. This project will build on top of these previous findings and look to
find solutions that will expand the current known interactions of these magnetized spheres.