14 citations · 18 across the 7 of their papers we have counts for
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math.DG2020★ 14 cited
Bicycle paths, elasticae and sub-Riemannian geometry
Andrey Ardentov, Gil Bor, Enrico Le Donne +2
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 f…
math.OC2020★ 1 cited
Extremals for a series of sub-Finsler problems with 2-dimensional control via convex trigonometry
A. A. Ardentov, L. V. Lokutsievskiy, Yu. L. Sachkov
We consider a series of optimal control problems with 2-dimensional control lying in an arbitrary convex compact set . The considered problems are well studied for the case when…