Neutrally floating objects of density 1/2 in three dimensions
Mathematical Physics
2012-04-12 v1 Classical Analysis and ODEs
math.MP
Abstract
This paper is concerned with the Floating Body Problem of S. Ulam: the existence of objects other than the sphere, which can float in a liquid in any orientation. Despite recent results of F. Wegner pointing towards an affirmative answer, a full proof of their existence is still unavailable. For objects with cylindrical symmetry and density 1/2, the conditions of neutral floating are formulated as an initial value problem, for which a unique solution is predicted in certain cases by a suitable generalization of the Picard-Lindel\"of theorem. Numerical integration of the initial value problem provides a rich variety of neutrally floating shapes.
Cite
@article{arxiv.1204.2402,
title = {Neutrally floating objects of density 1/2 in three dimensions},
author = {Péter L. Várkonyi},
journal= {arXiv preprint arXiv:1204.2402},
year = {2012}
}