Programs and utility functions using the Symbolic Math Toolbox are
provided to analyze vectors and tensors in general curvilinear
coordinates. The programs perform the following functions:
1) runcoord plots intersecting coordinate surfaces for typical
2) runmetric computes and prints metric tensor properties for a
general curvilinear coordinate system
3) rundivcrl verifies agreement of numerical values of divergence and
curl of an arbitrary vector computed in both cartesian and curvilinear
4) runconic plots surfaces illustrating how intersections of a cone and
a plane produce conic section curves.
5) Testmetric computes properties for nine different coordinate systems
and places the output in runmetric.tst. The symbolic equations from
some of the examples are fairly complicated.
The programs employ a number of other functions to define several
coordinate systems (such as cylindrical, spherical, toroidal, conical,
parabolic, ellipsoidal, and oblate spheroidal) and to compute base
vectors, metric tensors, Christoffel symbols, covariant derivatives,
divergence, and curl.
Files readme.m and equations.m describe the workspace contents and
governing equations. These files consist completely of comments and
can be examined with either the help or the edit commands. A pdf.file
named TensorNotes presents derivations of the classical analytical