Bicycle paths, elasticae and sub-Riemannian geometry
Differential Geometry
2021-08-11 v2 Classical Analysis and ODEs
Metric Geometry
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).
Cite
@article{arxiv.2010.04201,
title = {Bicycle paths, elasticae and sub-Riemannian geometry},
author = {Andrey Ardentov and Gil Bor and Enrico Le Donne and Richard Montgomery and Yuri Sachkov},
journal= {arXiv preprint arXiv:2010.04201},
year = {2021}
}
Comments
12 figures