  In this work, we analyzed theoretically and experimentally the nonlinear
dynamics of a magnetic pendulum driven by a coil-magnet interaction. The force
between the magnetic elements and the resulting torque on the pendulum are
derived using both the magnetic charges interaction model and the
experimentally fitted interaction model. This enables the comparison between
the two models. The current in the coil is taken first as a sinusoidal current
and then as a square current. The comparison of the structure of each
interaction model is conducted and it appears that they give qualitatively
similar characteristics. The harmonic balance method is used to approximate the
frequency responses of the pendulum leading to both symmetric and asymmetric or
one-side (intrawell) oscillations. The two-parameters bifurcation diagrams are
plotted showing the different dynamical behaviors considering the current
amplitude and frequency as the control parameters. Good agreements are found
between our theoretical results and experimental ones.
