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.


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

DetailsDetails

  • To use , you first need to load the Vector Analysis Package using Needs["VectorAnalysis`"].
  • The scale factors are given by , where , , 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.

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

In[1]:=
Click for copyable input

Scale factors for cylindrical coordinates:

In[2]:=
Click for copyable input
Out[2]=

The Jacobian determinant is the product of the scale factors:

In[3]:=
Click for copyable input
Out[3]=