Curvilinear Coordinates

Programs are presented which use symbolic math, curvilinear coordinates, and tensor concepts.

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 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
     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 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
  formulas used.
>>

• Required Products: Symbolic Math Toolbox
• MATLAB release: MATLAB 7.0.1 (R14SP1)
• Other requirements: 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.

[Theophanes Raptis]

How is one supposed to use the curl function in numeric mode? Tried with
syms r t p cs2 real; names=[r t p];
X=[r*sin(t)*cos(p);r*sin(t)*sin(p);r*cos(t)];% Basis of Covariant Vectors

bcov = [[ cos(t), -r*sin(t), 0], [ sin(t), r*cos(t), 0], [ 0, 0, 1]];
        
        
% Christoffel Symbols of the Second Kind

cs2 = zeros(3,3,3);
       
cs2(:,:,1) = [[ 0, 0, 0], [ 0, -r, 0], [ 0, 0, 0]];
 
cs2(:,:,2) = [[ 0, 1/r, 0], [ 1/r, 0, 0], [ 0, 0, 0]];
 
cs2(:,:,3) = [[ 0, 0, 0], [ 0, 0, 0], [ 0, 0, 0]];
 
curls([1, 2 ,3],names,bcovar,cs2,tn)

and gives

>> curltst
??? The following error occurred converting from sym to double:
Error using ==> sym.double at 25
DOUBLE cannot convert the input expression into a double array.
If the input expression contains a symbolic variable, use the VPA function instead.

Error in ==> curltst at 11
cs2(:,:,1) = [[ 0, 0, 0], [ 0, -r, 0], [ 0, 0, 0]];