Equilibria of plane convex bodies
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2019
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| Subjects: | |
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| _version_ | 1866916359902855168 |
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| author | Allemann, Jonas Hungerbühler, Norbert Wasem, Micha |
| author_facet | Allemann, Jonas Hungerbühler, Norbert Wasem, Micha |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1909_05900 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Equilibria of plane convex bodies Allemann, Jonas Hungerbühler, Norbert Wasem, Micha Differential Geometry Classical Analysis and ODEs 52A10, 54C30, 53A04 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. |
| title | Equilibria of plane convex bodies |
| topic | Differential Geometry Classical Analysis and ODEs 52A10, 54C30, 53A04 |
| url | https://arxiv.org/abs/1909.05900 |