Search results for "53A04"

showing 2 items of 2 documents

Curves with constant curvature ratios

2004

Curves in ${\mathbb R}^n$ for which the ratios between two consecutive curvatures are constant are characterized by the fact that their tangent indicatrix is a geodesic in a flat torus. For $n= 3,4$, spherical curves of this kind are also studied and compared with intrinsic helices in the sphere.

Mathematics - Differential GeometryDifferential Geometry (math.DG)FOS: MathematicsMathematics::Metric GeometryMathematics::Differential GeometryMatemàtica53A04
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Bicycle paths, elasticae and sub-Riemannian geometry

2020

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).

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 formulasymbolsNonlinearity
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