Equilibria of plane convex bodies

Thursday, 12 September, 2019

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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.


Jonas Allemann
Norbert Hungerbühler
Micha Wasem