Capillary floating and the billiard ball problem

Details Capillary floating and the billiard ball problem Capillary floating and the billiard ball problem

2010-12-11

arxiv.org/abs/1012.2448v1

Mathematics

Differential Geometry

31 pages, 8 figures

Scientific paper

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.

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