       Stokes integral transformation with Mathematica ?

• To: mathgroup at smc.vnet.net
• Subject: [mg33190] Stokes integral transformation with Mathematica ?
• From: Justus Heimann <Heimann at ism.tu-berlin.de>
• Date: Thu, 7 Mar 2002 02:23:43 -0500 (EST)
• Organization: Technical University Berlin, Germany
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

I got problem with integral transformation. I like to transform the
integral over a flat quadrilateral panel surface (x,y)

Integrate[-z/((x - x0)^2 + (y - y0)^2 + z^2))^(3/2), {x, xmin, xmax),
{y, ymin, ymax}];

to an equivalent line integral along the for panel edges.

This transformation usually is refered to as Stokes integral
transformation rule:
Int[Dot[Curl[{f1, f2, f3}], {n1, n2, n3}], {x, xmin, xmax), {y, ymin,
ymax}] ->
Int[{f1, f2, f3}, {s, smin, smax)]
where F={f1, f2, f3} is a vector field, N={n1, n2, n3} is the normal to
the, say quadrilateral panel surface, and s is the path along the panel
edges.

Does anyone have experience with such a symbolic Stokes transformation
within Mathematica ? Does anyone know an example with Mathematica ?