Calculus of Variations and Geometric Measure Theory
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A. Ardentov - G. Bor - E. Le Donne - R. Montgomery - Y. Sachkov

Bicycle paths, elasticae and sub-Riemannian geometry

created by ledonne on 02 Dec 2020

[BibTeX]

preprint

Inserted: 2 dec 2020
Last Updated: 2 dec 2020

Year: 2020

ArXiv: 2010.04201 PDF

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).

Tags: GeoMeG

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