A Repulsively Interacting Array of Magnetic Pendulums

The motions and interaction forces in a system of repulsively interacting magnetic pendulums, the mechanical analog of an array of Josephson junctions, are investigated. The equations of motion for a pair of magnetic pendulums 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 mo- tion and validated experimentally. The results indicate that the analytical model can accurately predict the motions of the pendulum system.