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 
of the confocal quadrics passing through that point (in other words,having 
, 
, 
, and 
, 
, 
for the squares of their semimajor axes), then the equation of aGeodesic can be expressed in the form | (8) |
an arbitrary constant, and the Arc Length element 
is given by | (9) |
References
Eisenhart, L. P. A Treatise on the Differential Geometry of Curves and Surfaces. New York: Dover, pp. 236-241, 1960.
Forsyth, A. R. Calculus of Variations. New York: Dover, p. 447, 1960.
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