2015/03/28 by Roy H. Goodman, Aminur Rahman, Michael Bellanich +3 · 17 citations
Computer Science · Mathematics · Physics and Astronomy · #Ball (mathematics) #Classical mechanics #Equations of motion #Geometry #Mathematical analysis #Mathematics #Mechanics #Motion (physics) #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Phenomenon #Physics #Point (geometry) #Point particle #Quantum chaos and dynamical systems #Quantum mechanics #Resonance (particle physics) #nlin.CD #nlin.PS
paper · pdf · doi:10.1063/1.4917047
published in Chaos An Interdisciplinary Journal of Nonlinear Science 25(4), 043109 (American Institute of Physics) · 9 pages, 8 figures, link to one youtube video
arxiv created 2015/03/28 · openalex publication_date 2015/04/01 · arxiv updated 2015/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We describe a simple mechanical system, a ball rolling along a specially-designed landscape, which mimics the well-known two-bounce resonance in solitary wave collisions, a phenomenon that has been seen in countless numerical simulations but never in the laboratory. We provide a brief history of the solitary wave problem, stressing the fundamental role collective-coordinate models played in understanding this phenomenon. We derive the equations governing the motion of a point particle confined to such a surface and then design a surface on which to roll the ball, such that its motion will evolve under the same equations that approximately govern solitary wave collisions. We report on physical experiments, carried out in an undergraduate applied mathematics course, that seem to exhibit the two-bounce resonance.