Floating Bodies of Equilibrium I
Classical Physics
2007-05-23 v3 General Physics
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)
Keywords
Cite
@article{arxiv.physics/0203061,
title = {Floating Bodies of Equilibrium I},
author = {Franz Wegner},
journal= {arXiv preprint arXiv:physics/0203061},
year = {2007}
}
Comments
Latex, 17 pages, 11 figures; 'I' added to title, factor '3' added in eq. 86