Amplitude equations for mechanical analogues of Faraday and nonlinear optical rotations

What is the relationship between the propagation of a light wave in a Kerr medium in the presence of a magnetic field and the oscillation of a spherical pendulum on a rotating platform? We apply the general formalism of amplitude equations in order to explore both the nonlinear and the rotation-induced precession of these optical and mechanical experiments. Then, we explain the surprising analogies between the two physical phenomena.