Floating bodies in two dimensions without gravity

Abstract

In this paper we study the stability of equilibrium configurations for two-dimensional smooth convex bodies in the absence of gravity, focusing on one example in particular, the ellipse. We also begin to consider the floating configurations of bodies which are not strictly convex; that is, bodies that have one or more linear sides. We will show that a body cannot float in a stable equilibrium with the fluid interface intersecting the interior of a straight side in a single point, and then using this result we will proceed to study the stability of convex bodies comprised of only straight sides consequently deriving a necessary and sufficient condition for stable equilibrium of polygonal bodies. We illustrate our findings using the square as an example. Finally, we prove several results concerning the number of stable and unstable configurations for an n-sided regular polygon (n ≥ 3) including a result guaranteeing the existence of a stable global energy minimum provided the contact angle γ is not 0 or π. © 2011 American Institute of Physics.