Visualizing the Phase Space of Two Interacting Spherical Magnets via Lagrangian Descriptors

This thesis studies the motion of one spherical magnet sliding on another fixed spherical magnet. Although the setup is simple, the resulting motion can range from regular and predictable to chaotic as the energy increases. To understand this behavior, mathematical tools are used to visualize how all possible motions are organized in phase space. These methods reveal patterns such as stable regions, repeating motions, and chaotic trajectories. The results show how order and chaos coexist in this system and provide insight into how small changes in the initial conditions can lead to very different outcomes.