Title: Some reversing orbits for a rattleback model
Authors: G. Arioli, H. Koch
Abstract:   A physical rattleback is a toy that can exhibit counter-intuitive behavior when spun on a horizontal plate. Most notably, it can spontaneously reverse its direction of rotation. Using a standard mathematical model of the rattleback, we prove the existence of reversing motion, reversing motion combined with rolling, and orbits that exhibit such behavior repeatedly.
Paper: Preprint and program text

Video 1:    R-symmetric periodic reversing orbit (described in Theorem 2.1)
Video 2:    R-symmetric heteroclinic reversing orbit (described in Theorem 2.2)
Video 3:    RS-symmetric heteroclinic reversing orbit (described in Theorem 2.2)
Video 4:    RS'-symmetric periodic reversing roll-over orbit (described in Theorem 2.3)
Video 5:    RS'-symmetric periodic roll-over orbit (described in Theorem 3.1)