These programs should run with Student MATLAB or Professional MATLAB and the Symbolic Toolbox. The software was developed on a computer having 4Gbyte of RAM. Users should remember that symbolic output in some instances can be quite lengthy.
Curvilinear Coordinates description
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 coordinate systems 2) runmetric computes and prints metric tensor properties 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 coordinates 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 basevectors, 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 formulas used.
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