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In this case, the ellipsoid is invariant under a rotation around the third axis, and there are thus infinitely many ways of choosing the two perpendicular axes of the same length. If the third axis is shorter, the ellipsoid is an oblate spheroid; if it is longer, it is a prolate spheroid. If the three axes have the same length, the ellipsoid is ...
Spheroid. A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters. A spheroid has circular symmetry. If the ellipse is rotated about its major axis, the result is a prolate ...
Oblate spheroidal coordinates are a three-dimensional orthogonal coordinate system that results from rotating the two-dimensional elliptic coordinate system about the non-focal axis of the ellipse, i.e., the symmetry axis that separates the foci. Thus, the two foci are transformed into a ring of radius in the x - y plane.
An ellipsoidal dome is a dome (also see geodesic dome), which has a bottom cross-section which is a circle, but has a cupola whose curve is an ellipse. [1] There are two types of ellipsoidal domes: prolate ellipsoidal domes and oblate ellipsoidal domes. A prolate ellipsoidal dome is derived by rotating an ellipse around the long axis of the ...
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.
for both prolate and oblate spheroids. For spheres, F a x = F e q = 1 {\displaystyle F_{ax}=F_{eq}=1} , as may be seen by taking the limit p → 1 {\displaystyle p\rightarrow 1} . These formulae may be numerically unstable when p ≈ 1 {\displaystyle p\approx 1} , since the numerator and denominator both go to zero into the p → 1 ...
Prolate spheroidal coordinates are a three-dimensional orthogonal coordinate system that results from rotating the two-dimensional elliptic coordinate system about the focal axis of the ellipse, i.e., the symmetry axis on which the foci are located. Rotation about the other axis produces oblate spheroidal coordinates.
The firehose instability in an N-body simulation of a prolate elliptical galaxy. Time progresses top–down, from upper left to lower right. Initially, the long-to-short axis ratio of the galaxy is 10:1. After the instability has run its course, the axis ratio is approximately 3:1. Note the boxy shape of the final galaxy, similar to the shapes ...