Capillary floating and the billiard ball problem

TL;DR

This paper links capillary floating in neutral equilibrium to billiard ball problems, solving the billiard problem and characterizing cylinders that float neutrally at any orientation with constant contact angles.

Contribution

It introduces a novel connection between capillary floating and billiard dynamics, providing solutions and characterizations for floating cylinders with specific contact angles.

Findings

Characterized possible contact angles for floating cylinders.

Constructed an infinite family of non-round cylinders with neutral equilibrium.

Solved the billiard problem related to the orthogonal cross-sections.

Abstract

We establish a connection between capillary floating in neutral equilibrium and the billiard ball problem. This allows us to reduce the question of floating in neutral equilibrium at any orientation with a prescribed contact angle for infinite homogeneous cylinders to a question about billiard caustics for their orthogonal cross-sections. We solve the billiard problem. As an application, we characterize the possible contact angles and exhibit an infinite family of real analytic non-round cylinders that float in neutral equilibrium at any orientation with constant contact angles.