Floating Bodies of Equilibrium I

Franz Wegner

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Floating Bodies of Equilibrium I

Franz Wegner

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Abstract

A long cylindrical body of circular cross-section and homogeneous density may float in all orientations around the cylinder axis. It is shown that there are also bodies of non-circular cross-sections which may float in any direction. Apart from those found by Auerbach for rho=1/2 there are one-parameter families of cross-sections for rho not= 1/2 which have a p-fold rotation axis. For given p they exist for p-2 densities rho. There are strong indications, that for all p-2 densities one has the same family of cross-sections. (Proven in physics/0205059)

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Franz Wegner. 2002-07-16. Floating Bodies of Equilibrium I. https://arxiv.org/abs/physics/0203061

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