Floating Bodies of Equilibrium II
Classical Physics
2007-05-23 v2 General Physics
Abstract
In a previous paper (physics/0203061) ''Floating bodies of equilibrium I'' I have shown that there exist two-dimensional non-circular cross-sections of bodies of homogeneous densities rho not equal 1/2 which can float in any orientation in water, which have a p-fold rotation axis. For given p they exist for p-2 different densities. However, this was found only in a Taylor-expansion in a parameter which describes the distortion from the circular shape up to seventh order. Here a differential equation for the boundary curve is given and the non-circular boundary curve can be expressed in terms of an elliptic integral.
Cite
@article{arxiv.physics/0205059,
title = {Floating Bodies of Equilibrium II},
author = {Franz Wegner},
journal= {arXiv preprint arXiv:physics/0205059},
year = {2007}
}
Comments
Latex, 12 pages, 4 figures; figure 3 reflected, two signs corrected