English: Unstable umbilical geodesic on a triaxial ellipsoid. Vital statistics: a:b:c = 1.01:1:0.8, β₁ = 90°, ω₁ = 0°, α₁ = 135° (i.e., normal to the plane y = 0), s₁₂/b ∈ [−142.6, 142.6], orthographic projection from φ = 40°, λ = 30°. The geodesic is found by solving the ordinary differential equations for the free motion of a particle constrained to the surface of the ellipsoid; the solution is carried out in Cartesian coordinates. See also