Equilibria of plane convex bodies

Fuente: arXiv
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Main Authors: Allemann, Jonas, Hungerbühler, Norbert, Wasem, Micha
Format: Preprint
Published: 2019
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author Allemann, Jonas
Hungerbühler, Norbert
Wasem, Micha
author_facet Allemann, Jonas
Hungerbühler, Norbert
Wasem, Micha
contents We obtain a formula for the number of horizontal equilibria of a planar convex body $K$ with respect to a center of mass $O$ in terms of the winding number of the evolute of $\partial K$ with respect to $O$. The formula extends to the case where $O$ lies on the evolute of $\partial K$ and a suitably modified version holds true for non-horizontal equilibria.
format Preprint
id arxiv_https___arxiv_org_abs_1909_05900
institution arXiv
publishDate 2019
record_format arxiv
spellingShingle Equilibria of plane convex bodies
Allemann, Jonas
Hungerbühler, Norbert
Wasem, Micha
Differential Geometry
Classical Analysis and ODEs
52A10, 54C30, 53A04
We obtain a formula for the number of horizontal equilibria of a planar convex body $K$ with respect to a center of mass $O$ in terms of the winding number of the evolute of $\partial K$ with respect to $O$. The formula extends to the case where $O$ lies on the evolute of $\partial K$ and a suitably modified version holds true for non-horizontal equilibria.
title Equilibria of plane convex bodies
topic Differential Geometry
Classical Analysis and ODEs
52A10, 54C30, 53A04
url https://arxiv.org/abs/1909.05900