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JacobianMatrix

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.

MORE INFORMATION

To use JacobianMatrix, you first need to load the Vector Analysis Package using Needs["VectorAnalysis`"].

The Jacobian matrix consists of the elements m_{i, j}=_{u_j}r_i where r₁, r₂, r₃ are the Cartesian coordinates x, y, z and 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.

Basic Examples (1)

Needs["VectorAnalysis`"]

Jacobian matrix for transformation from cylindrical to Cartesian coordinates:

Out[2]//MatrixForm=

Determinant for this transformation:

JacobianDeterminant ArcLengthFactor ScaleFactors Div Curl Grad Laplacian Biharmonic DotProduct CrossProduct ScalarTripleProduct

Vector Analysis Package

Vector Analysis Package

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