Equilibria of plane convex bodies

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.

arXiv comment21 pages, 8 figures

References in corpus (2)

• Non-integer valued winding numbers and a generalized Residue Theorem
• An integral that counts the zeros of a function