Elliptic Cylindrical Coordinates

[nassboy]

Is there a cylindrical coordinate system that is centered about the foci of an ellipse. It would include (r,theta,z) just like cylindrical coordinates only for an ellipse.

If this coordinate system exists, what is the laplacian?

Chris

 

[Civilized]

http://en.wikipedia.org/wiki/Elliptic_cylindrical_coordinates

Laplacian is the last equation, scroll down.

 

[nassboy]

I wasn't sure if those coordinate systems were exactly what I wanted...they aren't focci centered.

 

[Vortexman]

Can't you just perform a simple affine transformation so that the origin is at one of the foci? Of course, using the chain rule to incorporate this shift would slightly alter the form of your Laplacian.