2020/07/09 by S. Masalovich, Masalovich, Sergey
Physics and Astronomy · #Classical Physics (physics.class-ph) #Experimental and Theoretical Physics Studies #FOS: Physical sciences #Optics (physics.optics) #Quantum chaos and dynamical systems #Scientific Research and Discoveries
paper · doi:10.48550/arxiv.2007.04730
openalex publication_date 2020/07/09 · openalex created_date 2020/07/16 · openalex updated_date 2026/07/28
We propose geometric tools that are suitable for studying the behavior of a billiard trajectory in a homogeneous force field. Two examples are considered: a vertical plane with an open top and with a parabolic or right angle boundary at the bottom. In either case, we obtain equations that describe the envelope of a trajectory. These equations are in good agreement with those found earlier with the use of other calculation methods. In addition, we present some new geometric properties of trajectories. We show that in the case of a parabolic boundary the sequence of the trajectory impact points can be easily constructed by multiple reflections of a single ellipse.