## Ellipsoid Geodesic

An Ellipsoid can be specified parametrically by

 (1) (2) (3)

The Geodesic parameters are then
 (4) (5) (6)

When the coordinates of a point are on the Quadric
 (7)

and expressed in terms of the parameters and of the confocal quadrics passing through that point (in other words, having , , , and , , for the squares of their semimajor axes), then the equation of a Geodesic can be expressed in the form

 (8)

with an arbitrary constant, and the Arc Length element is given by

 (9)

where upper and lower signs are taken together.