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

• 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)

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Find the arc length factor of a helix:

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

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