CoordinateTransformData

CoordinateTransformData[t, property]
gives the value of the specified property for the coordinate transformation t.

CoordinateTransformData[t, property, {x1, x2, ..., xn}]
gives the value of the property evaluated at the point .

DetailsDetails

  • Transformations can be entered in the form , where oldchart and newchart are valid chart specifications available from CoordinateChartData.
  • Coordinate transformation standard names are triples of the form , where and are valid charts available from CoordinateChartData.
  • CoordinateTransformData[] gives a list of available coordinate transformations, including only low-dimensional members of infinite families.
  • CoordinateTransformData[t] is equivalent to CoordinateTransformData[t, "StandardName"].
  • CoordinateTransformData["Properties"] returns a list of available properties.
  • When no evaluation point is specified, properties are typically pure functions expecting a list of length n.
  • Available properties include:
  • "Mapping"mapping from old to new coordinates
    "MappingJacobian"Jacobian matrix of the mapping
    "MappingJacobianDeterminant"determinant of the mapping Jacobian matrix
    "InverseMappingJacobian"inverse of the Jacobian matrix of the mapping
    "OrthonormalBasisRotation"rotation matrix between the orthonormal bases of the charts
    "StandardName"Mathematica standard name

ExamplesExamplesopen allclose all

Basic Examples (1)Basic Examples (1)

Conversion between spherical and Cartesian coordinates in three dimensions:

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