Neutrally floating objects of density 1/2 in three dimensions

Details Neutrally floating objects of density 1/2 in three dimensions Neutrally floating objects of density 1/2 in three dimensions

2012-04-11

arxiv.org/abs/1204.2402v1

Physics

Mathematical Physics

Scientific paper

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.

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