ArcCurvature

ArcCurvature[{x1,,xn},t]

gives the curvature of the parametrized curve whose Cartesian coordinates xi are functions of t.

ArcCurvature[{x1,,xn},t,chart]

interprets the xi as coordinates in the specified coordinate chart.

Details • The arc curvature is sometimes referred to as the unsigned or Frenet curvature.
• The arc curvature of the curve in three-dimensional Euclidean space is given by .
• In a general space, the arc curvature of the curve is given by .
• In ArcCurvature[x,t], if x is a scalar expression, ArcCurvature gives the curvature of the parametric curve {t,x}.
• Coordinate charts in the third argument of ArcCurvature can be specified as triples {coordsys,metric,dim} in the same way as in the first argument of CoordinateChartData. The short form in which dim is omitted may be used.

Examples

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Basic Examples(2)

A circle has constant curvature:

 In:= Out= The curvature of Fermat's spiral expressed in polar coordinates:

 In:= Out= In:= Out= Visualize both branches of the curve:

 In:= Out= Properties & Relations(2)

Introduced in 2014
(10.0)