A Billiard Problem in Nonlinear Dissipative Systems

A Billiard Problem in Nonlinear Dissipative Systems
English | 2026 | ISBN: 9819575605 | 147 Pages | PDF EPUB (True) | 24 MB
This book addresses a new class of billiard problems, focusing on the motion of a self-propelling disk in a nonlinear dissipative system on a rectangular domain. Unlike classical billiards, which have been extensively studied in mathematics, this setting introduces unique dynamics inspired by experiments with camphor disks floating on water-a well-known phenomenon in nonlinear science. Laboratory observations reveal two striking properties: (i) the disk reflects without physical collision at the boundary, and (ii) the reflection angle exceeds the incidence angle, differing from the perfect elastic reflection of classical billiards. These features suggest that the behavior of a self-propelling disk is fundamentally distinct from classical billiard motion.