On the equilibria of finely discretized curves and surfaces

Domokos, Gábor and Lángi, Zsolt and Szabó, Tímea (2011) On the equilibria of finely discretized curves and surfaces. Monatshefte für Mathematik, 168 (3). pp. 321-345. ISSN 0026-9255


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Our goal is to identify the type and number of static equilibrium points of solids arising from fine, equidistant n-discretizations of smooth, convex surfaces. We assume uniform gravity and a frictionless, horizontal, planar support. We show that as n approaches infinity these numbers fluctuate around specific values which we call the imaginary equilibrium indices associated with the approximated smooth surface. We derive simple formulae for these numbers in terms of the principal curvatures and the radial distances of the equilibrium points of the solid from its center of gravity. Our results are illustrated on a discretized ellipsoid and match well the observations on natural pebble surfaces.

Item Type: Article
Subjects: Q Science / természettudomány > QA Mathematics / matematika > QA73 Geometry / geometria
Depositing User: Dr. Zsolt Lángi
Date Deposited: 11 Sep 2015 11:02
Last Modified: 11 Sep 2015 11:02

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