  The magnetostatic energy is calculated for a magnetic vortex in a noncircular
elliptical nanodisk. It is well-known that the energy of a vortex in the
circular disk is minimized though an ansatz that eliminates the magnetostatic
charge at the disk edge. Beginning with this ansatz for the circular disk, a
conformal mapping of a circle interior onto the interior of an ellipse results
in the magnetization of the elliptical disk. This magnetization in the interior
of an ellipse also has no magnetostatic charge at the disk edge also minimizing
the magnetostatic energy. As expected the energy has a quadratic dependence on
the displacement of the vortex core from the ellipse center, but reflecting the
lower symmetry of the ellipse. Through numerical integration of the
magnetostatic integral a general expression for the energy is obtained for
ellipticity values from 1.0 to about 0.3. Finally a general expression for the
gyrotropic frequency as described by the Thiele equation is obtained.
