Frequently, physical systems exhibit special symmetries or structures that make a particular coordinate system especially useful. In a mathematically elegant solution to problems related to these systems, often the main step is choosing the correct coordinates. A variety of tools for doing calculus in various three-dimensional coordinate systems are provided in this package.
SetCoordinates — set the default coordinate system
CoordinateSystem — default coordinate system
Coordinates — default variables in the default coordinate system
CoordinateRanges — interval over which the coordinate variables range
Parameters — default parameters of the coordinate system
ParameterRanges — range of values of the parameters of the coordinate system
Coordinate Transformations
CoordinatesToCartesian — transform coordinates to Cartesian coordinates
CoordinatesFromCartesian — transform coordinates from Cartesian coordinates
ArcLengthFactor — derivative of the arc length along parameterized curve
JacobianMatrix — derivative matrix of the coordinate transformation
JacobianDeterminant — determinant of the Jacobian matrix
ScaleFactors — list the scale factors
