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The study of geodesics on an ellipsoid arose in connection with geodesy specifically with the solution of triangulation networks. The figure of the Earth is well approximated by an oblate ellipsoid, a slightly flattened sphere. A geodesic is the shortest path between two points on a curved surface, analogous to a straight line on a plane surface.
English: Transpolar geodesic on a triaxial ellipsoid, case A. Vital statistics: a:b:c = 1.01:1:0.8, β 1 = 90°, ω 1 = 39.9°, α 1 = 180°, s 12 /b ∈ [−232.7, 232.7], 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 ...
In geodesy, a map projection of the triaxial ellipsoid maps Earth or some other astronomical body modeled as a triaxial ellipsoid to the plane. Such a model is called the reference ellipsoid. In most cases, reference ellipsoids are spheroids, and sometimes spheres. Massive objects have sufficient gravity to overcome their own rigidity and ...
Klein quartic with 28 geodesics (marked by 7 colors and 4 patterns). In geometry, a geodesic (/ ˌ dʒ iː. ə ˈ d ɛ s ɪ k,-oʊ-,-ˈ d iː s ɪ k,-z ɪ k /) [1] [2] is a curve representing in some sense the locally [a] shortest [b] path between two points in a surface, or more generally in a Riemannian manifold.
English: Circumpolar geodesic on a triaxial ellipsoid, case A. Vital statistics: a:b:c = 1.01:1:0.8, β 1 = 45.1°, ω 1 = 0°, α 1 = 90°, s 12 /b ∈ [−321.9, 321.9], 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 ...
English: Circumpolar geodesic on a triaxial ellipsoid, case B. Vital statistics: a:b:c = 1.01:1:0.8, β 1 = 87.48°, ω 1 = 0°, α 1 = 90°, s 12 /b ∈ [−491.6, 491.6], 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 ...
English: Transpolar geodesic on a triaxial ellipsoid, case B. Vital statistics: a:b:c = 1.01:1:0.8, β 1 = 90°, ω 1 = 9.966°, α 1 = 180°, s 12 /b ∈ [−508.8, 508.8], 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 ...
Triaxial ellipsoidal coordinates. Add languages. Add links. Article; ... Geodesics on an ellipsoid#Triaxial ellipsoid coordinate system; Retrieved from "https: ...