CoordinateChartData

CoordinateChartData[chart, property]
gives the value of the specified property for chart.

CoordinateChartData[chart, property, {x1, x2, ..., xn}]
gives the value of the specified property for chart evaluated at the point .

DetailsDetails

  • A coordinate chart may be specified by a coordinate system name, by a pair , or by a standard name of the form . The dimension dim is a positive integer. Pairs are interpreted as referring to the Euclidean metric.
  • Valid metric specifications include:
  • "metric"metric with default parameter values
    {"metric",param}metric with a single parameter specified
    {"metric",{param1,param2,...}}metric with several parameters specified
  • Valid coordinate system specifications include:
  • "coordsys"coordinate system with default parameter values
    {"coordsys",param}coordinate system with a single parameter specified
    {"coordsys",{param1,param2,...}}coordinate system with several parameters specified
  • If an evaluation point is given, the dimension n may be omitted from the coordinate chart name in the first argument.
  • Any or all of the elements of the triple in can be replaced with the symbol All. In this case, CoordinateChartData[chart, property] will return a list of values for the coordinate charts that match the specified elements.
  • CoordinateChartData[] gives a list of available coordinate charts, including only low-dimensional members of infinite families.
  • CoordinateChartData[chart] is equivalent to CoordinateChartData[chart, "StandardName"].
  • CoordinateChartData["Properties"] returns a list of available properties.
  • When no evaluation point is specified, properties are typically pure functions expecting a list of length n.
  • Basic properties include:
  • "AlternateCoordinateNames"common alternate coordinate names, as strings, used for the chart
    "CoordinateRangeAssumptions"logical expression for the assumptions satisfied by the coordinates of the chart
    "Dimension"dimension
    "ParameterRangeAssumptions"logical expression for the assumptions satisfied by the parameters of the chart
    "StandardCoordinateNames"the names, as strings, of the most common coordinate names used for the chart
    "StandardName"Mathematica standard name
  • Metric-related properties include:
  • "InverseMetric"components of the inverse (contravariant) metric tensor in the coordinated basis
    "Metric"components of the metric tensor in the coordinated basis
    "ScaleFactors"scale factors, as a list, of an orthogonal chart
    "VolumeFactor"coefficient of the differential in volume integrals
  • In Euclidean coordinate charts with integer n, valid coordsys values include:
  • "Cartesian"Cartesian coordinates for
    "Hyperspherical"spherical coordinates with poles along the axis for , and polar coordinates for
    {"Confocal", {a1,...,an}}confocal coordinates with semimajor axes for , and coordinates bounded from below in increasing order
  • In two-dimensional Euclidean coordinate charts , valid coordsys values include:
  • "Polar"polar coordinates
    {"Bipolar",{a}}
  • bipolar coordinates with focal length in the order focal angle, logarithmic radius
  • {"Elliptic", {a}}elliptic coordinates with focal length in the order hyperbolic radius, azimuthal angle
    "PlanarParabolic"two-dimensional parabolic coordinates
  • In three-dimensional Euclidean coordinate charts , valid coordsys values include:
  • "Cylindrical"polar-cylindrical coordinates
    "Spherical"spherical coordinates with poles along the axis and coordinates in the order radius, polar angle, azimuthal angle
    {"BipolarCylindrical",{a}}bipolar-cylindrical coordinates with focal length in the order focal angle, logarithmic radius,
    {"Bispherical",{a}}bispherical coordinates with focal length in the order focal angle, logarithmic radius, azimuthal angle
    "CircularParabolic"parabolic coordinates with the last coordinate azimuthal angle
    {"ConfocalParaboloidal", {a,b}}confocal paraboloidal coordinates centered on the axis with , coordinates positive in increasing order
    {"Conical",{b,c}}conical coordinates with parameters
    {"EllipticCylindrical", {a}}elliptic-cylindrical coordinates with focal length in the order hyperbolic radius, azimuthal angle,
    {"OblateSpheroidal",{a}}oblate spheroidal coordinates with focal length in the order hyperbolic radius, polar angle, azimuthal angle
    "ParabolicCylindrical"parabolic-cylindrical coordinates
    {"ProlateSpheroidal",{a}}prolate spheroidal coordinates with focal length in the order hyperbolic radius, polar angle, azimuthal angle
    {"Toroidal",a}toroidal coordinates with ring radius in the order logarithmic radius, focal angle, azimuthal angle
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