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On a triaxial ellipsoid, there are only three simple closed geodesics, the three principal sections of the ellipsoid given by X = 0, Y = 0, and Z = 0. [7] To survey the other geodesics, it is convenient to consider geodesics that intersect the middle principal section, Y = 0 , at right angles.
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 ...
The general ellipsoid, also known as triaxial ellipsoid, is a quadratic surface which is defined in Cartesian coordinates as: ... Geodesics on an ellipsoid;
A triaxial ellipsoid and its three geodesics. A geodesic, on a Riemannian surface, is a curve that is locally straight at each of its points. On the Euclidean plane the geodesics are lines, and on a sphere the geodesics are great circles. The shortest path in the surface between two points is always a geodesic, but other geodesics may exist as ...
A geodesic on a triaxial ellipsoid. If an insect is placed on a surface and continually walks "forward", by definition it will trace out a geodesic. The most familiar examples are the straight lines in Euclidean geometry. On a sphere, the images of geodesics are the great circles.
Triaxial ellipsoidal coordinates. Add languages. Add links. Article; ... Geodesics on an ellipsoid#Triaxial ellipsoid coordinate system; Retrieved from "https: ...
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 ...
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