6533b7ddfe1ef96bd1275319

RESEARCH PRODUCT

Bicycle paths, elasticae and sub-Riemannian geometry

Richard MontgomeryGil BorEnrico Le DonneEnrico Le DonneA. A. ArdentovYuri L. Sachkov

subject

Mathematics - Differential GeometryGeodesicGeneral Physics and AstronomyGeometryRiemannian geometry01 natural sciencessymbols.namesakeMathematics - Metric GeometryClassical Analysis and ODEs (math.CA)FOS: Mathematics0101 mathematicsMathematical PhysicsMathematics53C17 (Primary) 53A17 53A04 (Secondary)Group (mathematics)Plane (geometry)Applied Mathematics010102 general mathematicsMetric Geometry (math.MG)Statistical and Nonlinear Physics010101 applied mathematicsDifferential Geometry (math.DG)Mathematics - Classical Analysis and ODEsMetric (mathematics)Euler's formulasymbols

description

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).

yearjournalcountryeditionlanguage
2020-10-08Nonlinearity
10.1088/1361-6544/abf5bfhttp://dx.doi.org/10.1088/1361-6544/abf5bf