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arXiv · 0706.0119

Towards a Completion of Archimedes' Treatise on Floating Bodies

Kurt Girstmair·Gerhard Kirchner
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Abstract

In his treatise on floating bodies Archimedes determines the equilibrium positions of a floating paraboloid segment, but only in the case when the basis of the segment is either completely outside of the fluid or completely submerged. Here we give a mathematical model for the remaining case, i.e., two simple conditions which describe the equilibria in closed form. We provide tools for finding all equilibria in a reliable way and for the classification of these equilibria. This paper can be considered as a continuation of a recent article of Rorres.

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Kurt Girstmair, Gerhard Kirchner. 2007-06-01. Towards a Completion of Archimedes' Treatise on Floating Bodies. https://arxiv.org/abs/0706.0119

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