2007/11/23 by Stefano Pasquero, Pasquero, Stefano
Engineering · Physics and Astronomy · #Classical Physics (physics.class-ph) #Dynamics and Control of Mechanical Systems #FOS: Physical sciences #Quantum chaos and dynamical systems #Sports Dynamics and Biomechanics #physics.class-ph
paper · pdf · doi:10.48550/arxiv.0711.3698
9 pages
arxiv created 2007/11/23 · openalex publication_date 2007/11/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We analyze the impact of two equal billiard balls in three ideal situations: when the balls freely slide on the plane of the billiard, when they roll without sliding and when one of them freely slides and the other rolls. In all the cases we suppose that the contact between the balls is smooth. We base our analysis on some recent general theoretical results on ideal impacts obtained by means of Differential Geometric Impulsive Mechanics. We use symbolic computation software to solve the computational difficulties arising by the high number of degrees of freedom of the system. Some particular but significative impacts, with opportunely assigned left velocities and positions of the balls, are analyzed in details. The results admit easy interpretations that turn out to be in good agreement with the reasonable forecasts and the behaviours of real systems.