Conceptual

Nonlinear Magnetic Pendulum Dynamics with Position-Dependent Excitation Phase

A single-degree-of-freedom pendulum carrying a permanent magnet and driven by a coil current, modeled by a Newton-Euler equation of motion combining gravity, a linear spring, Stribeck (Coulomb-plus-static) friction, and a Gaussian magnetic-torque term whose sinusoidal driving phase is made a linear function of the pendulum's angular position. Recast in dimensionless form and studied by numerical bifurcation diagrams and the largest Lyapunov exponent, the system displays coexisting periodic attractors, rich multistability, and period-doubling routes to chaos, with simulated phase trajectories closely matching experiment.