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Inspired by the self-propelled, billiard-like motion of a camphor disk floating on the surface of water, we motivate and introduce three mathematical models. Our camphor disk moves in a straight line and reflects as it approaches the boundary of the tank, somewhat like a billiard ball, but exhibits nonspecular reflection. It loses speed on reflection, but then it recovers its speed. How does it behave if it is confined to a square domain? In contrast to classical billiards, it seems that its asymptotic orbit is determined almost independently of the initial condition in the case of a camphor disk.

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Introduction

  • 章节

  • 发表日期：

    2026年

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  • Tomoyuki Miyaji,
  • Shin-Ichiro Ei,
  • Masayasu Mimura

摘要

Inspired by the self-propelled, billiard-like motion of a camphor disk floating on the surface of water, we motivate and introduce three mathematical models. Our camphor disk moves in a straight line and reflects as it approaches the boundary of the tank, somewhat like a billiard ball, but exhibits nonspecular reflection. It loses speed on reflection, but then it recovers its speed. How does it behave if it is confined to a square domain? In contrast to classical billiards, it seems that its asymptotic orbit is determined almost independently of the initial condition in the case of a camphor disk.