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arXiv · 1909.05900

Equilibria of plane convex bodies

Jonas Allemann·Norbert Hungerbühler·Micha Wasem
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Abstract

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.

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Jonas Allemann, Norbert Hungerbühler, Micha Wasem. 2019-09-12. Equilibria of plane convex bodies. https://doi.org/10.1007/s00332-021-09740-2

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