Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4582595 | Expositiones Mathematicae | 2008 | 18 Pages |
Abstract
In the said treatise 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 Rorres's article [C. Rorres, Completing book II of Archimedes's on floating bodies, Math. Intell. 26(3) (2004) 32–42].
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Kurt Girstmair, Gerhard Kirchner,