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Equilibria of plane convex bodies

Allemann, Jonas; Hungerbühler, Norbert; Wasem, Micha
2021
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Résumé

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 ∂K with respect to O. The formula extends to the case where O lies on the evolute of ∂K and a suitably modified version holds true for non-horizontal equilibria.

Détails

Titre
Equilibria of plane convex bodies
Auteur(s)/ trice(s)
Allemann, Jonas (IBM, Zürich, Switzerland)
Hungerbühler, Norbert (ETH Zürich, Zürich, Switzerland)
Wasem, Micha (School of Engineering and Architecture (HEIA-FR), HES-SO University of Applied Sciences Western Switzerland)
Date
2021-08
Publié dans
Journal of Nonlinear Science
Volume
2021, vol. 31, article no. 86
Pagination & équivalents
19 p.
DOI
https://doi.org/10.1007/s00332-021-09740-2
ISSN
0938-8974
Mots-clés (libres)
static equilibria ; convex bodies ; gömböc
Type d'article
scientifique
Domaine
Ingénierie et Architecture
Ecole
HEIA-FR
Institut
iSIS - Institut des systèmes intelligents et sécurisés
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