Reflection of a self-propelling rigid disk from a boundary

Abstract

A system of ordinary differential equations that describes the motion of a self-propelling rigid disk is studied. In this system, the disk moves along a straight-line and reflects from a boundary. Interestingly, numerical simulation shows that the angle of reflection is greater than that of incidence. The purpose of this study is to present a mathematical proof for this attractive phenomenon. Moreover, the reflection law is numerically investigated. Finally, existence and asymptotic stability of a square-shaped closed orbit for billiards in square table with inelastic reflection law are discussed.