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ArcLengthFactor

ArcLengthFactor[{f1,f2,f3},t]

gives the derivative of the arc length of the curve described by the parametrized curve coordinates {f1,f2,f3} with respect to the parameter t in the default coordinate system.

ArcLengthFactor[{f1,f2,f3},t,coordsys]

gives the derivative of the arc length of a curve in the coordinate system coordsys.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
See Also
Tech Notes
Related Guides
VectorAnalysis`
VectorAnalysis`

ArcLengthFactor

As of Version 9.0, vector analysis functionality is built into the Wolfram Language »

ArcLengthFactor[{f1,f2,f3},t]

gives the derivative of the arc length of the curve described by the parametrized curve coordinates {f1,f2,f3} with respect to the parameter t in the default coordinate system.

ArcLengthFactor[{f1,f2,f3},t,coordsys]

gives the derivative of the arc length of a curve in the coordinate system coordsys.

Details and Options

  • To use ArcLengthFactor, you first need to load the Vector Analysis Package using Needs["VectorAnalysis`"].
  • The parametrized curve coordinates {f1,f2,f3} should be given in coordsys, if specified, or the default coordinate system otherwise.
  • If the parametrized curve coordinates {f1,f2,f3} are not given, the default coordinate variables for coordsys are used.
  • Integrate[ArcLengthFactor[{f1,f2,f3},t],{t,t1,t2}] gives the length of the arc described by {f1,f2,f3} from t1 to t2.

Examples

Basic Examples  (1)

Wolfram Language code: Needs["VectorAnalysis`"]

Find the arc length factor of a helix:

Wolfram Language code: Helix = {2 Cos[t], 2Sin[t], t ^ 2 / 39};
Wolfram Language code: ParametricPlot3D[Helix, {t, 0, 20}]
Wolfram Language code: a = ArcLengthFactor[Helix, t]//Simplify

Compute the arc length of the helix from t=0 to t=20:

Wolfram Language code: Integrate[a, {t, 0, 20}]