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arXiv · 2010.04201

Bicycle paths, elasticae and sub-Riemannian geometry

Andrey Ardentov·Gil Bor·Enrico Le Donne·Richard Montgomery·Yuri Sachkov
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Abstract

We relate the sub-Riemannian geometry on the group of rigid motions of the plane to `bicycling mathematics'. We show that this geometry's geodesics correspond to bike paths whose front tracks are either non-inflectional Euler elasticae or straight lines, and that its infinite minimizing geodesics (or `metric lines') correspond to bike paths whose front tracks are either straight lines or `Euler's solitons' (also known as Syntractrix or Convicts' curves).

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Andrey Ardentov, Gil Bor, Enrico Le Donne, Richard Montgomery, Yuri Sachkov. 2020-10-08. Bicycle paths, elasticae and sub-Riemannian geometry. https://doi.org/10.1088/1361-6544/abf5bf

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