  We use a third-order perturbation theory and Melnikov's method to prove the
existence of chaos in spinning circular disks subject to a lateral point load.
We show that the emergence of transverse homoclinic and heteroclinic points
respectively lead to a random reversal in the traveling direction of
circumferential waves and a random phase shift of magnitude $\pi$ for both
forward and backward wave components. These long-term phenomena occur in
imperfect low-speed disks sufficiently far from fundamental resonances.
