Can the symbolic toolbox Laplacian be used for other than cartesian coordinates?

In potential theory and elasticity theory, the Laplacian operator often appears, and is applied in all separable (orthogonal)

coordinate systems. The Laplacian-squared (del-fourth) operator also appears in elasticity theory. I know that the

Symbolic Toolbox Laplacian can be applied in cartesian coordinates (and that symbolic divergence, gradient, and

curl operators exist) but how about for other orthogonal coordinate systems such as polar, cylindrical,

spherical, elliptical, etc.? How about for the Laplacian-squared operator - has anyone tackled this even for

cartesian coordinates?

Answer 1

[Tanmay Das]

Hi,

In the current scenario, I suppose there are no functions for Polar or cylindrical Laplacian. However, the developers are aware of this case. Meanwhile, you can try converting other coordinate systems into cartesian coordinate system and then use laplacian function if that is possible.

[Ken Bannister]

Tanmay - Thanks for your reply. I believe you are correct and that is a good work-around. I know that with Mathematica, the Laplacian is done in cartesian, and then they recommend (and give examples) doing a transformation of coordinates to get it into other coordinate systems. In principle that should work. I have a table showing the details for polar, cyclindrical, spherical, and a few other coordianate systems. I need to try this out with MATLAB and see how it goes.