Geodesic on an Ellipsoid

Geodesic equations on oblate spheroid (semi-axes a, b=a(1-f)):
Clairaut's relation: r·sin(α) = const, where r = distance from axis, α = azimuth angle.
The geodesic oscillates between latitudes φ_min and φ_max (like a pendulum in φ). Longitude advance per half-period on ellipsoid < π (sphere), causing westward precession of the equatorial crossing. Blue = geodesic on ellipsoid; green dashes = great circle on sphere for comparison.