Curl in Polar Coordinates

Hello All,

I was wondering if anyone knows of an m-file that can calculate the curl in polar coordinates. I have all x,y,z,u,v,w data in Cartesian coordinates and should be able to convert it to polar without a problem, but I don't know where to go from there.

Thanks,

Spence

Answer 1

[Paulo Silva]

doc cart2pol

Answer 2

[Bjorn Gustavsson]

I think it is easiest to calculate the curl in Cartesian coordinates and then transform the result to polar coordinates. Especially as you have the data in Cartesian coordinates. Then you avoid the hassle of doing the non-Cartesian curl, and one interpolation...

Answer 3

[Wiky]

The below function calculates the "CURL" of a vector field in all three coordinate systems.i.e Rectangular, Cylindrical and Spherical.

Where V is field vector, X spacial vector.

%%%%%%%%%%%%%% Code of Curl in Polar Coordinates %%%%%%%%%%%%%%%

function Curl = Curl_sym(V,X,coordinate_system)

switch coordinate_system

case {'cartesian','Cartesian'}

Curl=curl(V,X);

case {'cylindrical','Cylindrical'}

Curl = [(1/X(1))*diff(V(3),X(2))-diff(V(2),X(3)), diff(V(1),X(3))-diff(V(3),X(1)), (1/X(1))*diff(X(1)*V(2),X(1))-diff(V(1),X(2))];

case {'spherical','Spherical'}

Curl = [(1./X(1)*diff(V(3),X(2))-diff(V(2),X(3))) (diff(V(1),X(3))-diff(V(3),X(1))) 1./X(1)*(diff(X(1).*V(2),X(1))-diff(V(1),X(2)))];

end

end