Bicycle Wheel Pendulum - Coupled Oscillator

A wheel is rotated suspended from a rope. It is (almost perfectly) tuned as a variant of a Wilberfoce pendulum, coupled oscillator. It changes from upright circular motion with no pendulum swing, to a flat circular motion with a large swing and back. I think that it's precession becomes pendulum motion, and the wheel goes flat. Because of the swing, the flat circle feels a gyroscopic force and rises once again to the upright position at the expense of the pendulum motion. Please figure out the normal modes and the equations of motion for this system. I've never seen it discussed in the literature.