A Repulsively Interacting Array of Magnetic Pendulums

Abstract

Abstract. The motions of a system of repulsively interacting magnetic pendulums and their interaction forces are investigated. The equations of motion for the pendulum array are formulated including geometrically accurate closed-form expressions for the magnetic interaction forces. The equilibrium points, natural frequencies, and nonlinear oscillations of the system are predicted using the equations of motion and validated experimentally. The results indicate that the analytical model can accurately predict the motions of the pendulum system. This system is of intrinsic value for the rich dynamic phenomena it reveals. It is also of interest as a simple mechanical analog of quantum and other hard to realize dynamic systems.