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) |
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