ScaleFactors

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

ScaleFactors[pt]

gives a list of the scale factors at the point pt in the default coordinate system.

ScaleFactors[pt,coordsys]

gives a list of the scale factors in the coordinate system coordsys.

Details and Options

To use ScaleFactors, you first need to load the Vector Analysis Package using Needs["VectorAnalysis`"].
The scale factors are given by , where u₁, u₂, u₃ are the coordinates of the coordinate system coordsys, if specified, or the default coordinate system otherwise.
The coordinates of pt should be given in the coordinate system coordsys, if specified, or the default coordinate system otherwise.
If pt is not given, the default coordinate variables for coordsys are used.

Scale factors for cylindrical coordinates:

The Jacobian determinant is the product of the scale factors:

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