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.

MORE INFORMATION

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

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Basic Examples (1)

Needs["VectorAnalysis`"]

Arc length factor a helix:

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

In[5]:=

Out[5]=