VectorAnalysis`
VectorAnalysis`

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.

Examples

Basic Examples  (1)

Scale factors for cylindrical coordinates:

The Jacobian determinant is the product of the scale factors: