JacobianMatrix
VectorAnalysis`
VectorAnalysis`
JacobianMatrix
As of Version 9.0, vector analysis functionality is built into the Wolfram Language »
JacobianMatrix[pt]
gives the Jacobian matrix of the transformation from the default coordinate system to the Cartesian coordinate system at the point pt.
JacobianMatrix[pt,coordsys]
gives the Jacobian matrix of the transformation from the coordinate system coordsys to the Cartesian coordinate system at the point pt.
Details and Options
- To use JacobianMatrix, you first need to load the Vector Analysis Package using Needs["VectorAnalysis`"].
- The Jacobian matrix consists of the elements
where 
, 
, 
are the Cartesian coordinates and 
, 
, 
are the variables 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)
Needs["VectorAnalysis`"]Jacobian matrix for transformation from cylindrical to Cartesian coordinates:
JacobianMatrix[{Rr, Ttheta, Zz}, Cylindrical]//MatrixFormDeterminant for this transformation:
Det[%]//SimplifyJacobianDeterminant[{Rr, Ttheta, Zz}, Cylindrical]