Shape taken by a self-gravitating fluid body rotating at constant velocity
Artistic rendering of Haumea, a dwarf planet with triaxial ellipsoid shape.
A Jacobi ellipsoid is a triaxial (i.e. scalene) ellipsoid under hydrostatic equilibrium which arises when a self-gravitating, fluid body of uniform density rotates with a constant angular velocity. It is named after the German mathematician Carl Gustav Jacob Jacobi.[1]
^Jacobi, C. G. (1834). "Ueber die Figur des Gleichgewichts". Annalen der Physik (in German). 109 (8–16): 229–233. Bibcode:1834AnP...109..229J. doi:10.1002/andp.18341090808.
A Jacobiellipsoid is a triaxial (i.e. scalene) ellipsoid under hydrostatic equilibrium which arises when a self-gravitating, fluid body of uniform density...
freedom of motion. Jacobiellipsoid, a triaxial ellipsoid formed by a rotating fluid Crystallography Index ellipsoid, a diagram of an ellipsoid that depicts...
Carl Gustav Jacob Jacobi (/dʒəˈkoʊbi/; German: [jaˈkoːbi]; 10 December 1804 – 18 February 1851) was a German mathematician who made fundamental contributions...
centered on the ellipsoid and, without loss of generality, a ≥ b ≥ c > 0. Jacobi (1866, §§26–27) employed the (triaxial) ellipsoidal coordinates (with...
instability (and secular stability implies dynamic stability). Jacobiellipsoid Spheroid Ellipsoid Maclaurin, Colin. A Treatise of Fluxions: In Two Books. 1...
most recent models show that Psyche has a shape consistent with a Jacobiellipsoid and dimensions within a few km of 278 km x 238 km x 171 km. Each shape...
ellipsoid were developed by Maxim Nyrtsov. Jacobi conformal projections were described by Carl Gustav Jacob Jacobi. Geodesics on a triaxial ellipsoid...
calculations from its light curve are consistent with it being a Jacobiellipsoid (the shape it would be if it were a dwarf planet), with its major axis...
Vedic texts. Varuna's light curve is compatible with the body being a Jacobiellipsoid, suggesting that it has an elongated shape due to its rapid rotation...
statement of Jacobi is a conjecture named after Carl Gustav Jacob Jacobi, which states: Every caustic from any point p {\displaystyle p} on an ellipsoid other...
better modeled by triaxial ellipsoid or prolated spheroid with small eccentricities. Haumea's shape is a Jacobiellipsoid, with its major axis twice as...
in the liquid. In 1834, Carl Jacobi discovered his uniformly rotating self-gravitating ellipsoids (the Jacobiellipsoid). In 1834, John Russell observed...
respectively. In 1834, Carl Jacobi discovered his uniformly rotating self-gravitating ellipsoids (the Jacobiellipsoid). In 1834, John Russell observed...
gravitational and hydrostatic equilibrium. Jacobi and soon later Liouville, in 1834, discussed the fact that a tri-axial ellipsoid was an equilibrium solution for...
giving us a varying ellipsoid of constant energy. This is shown in the animation as a fixed orange ellipsoid and increasing blue ellipsoid. For concreteness...
reaches 0.3302). Above the critical value the solution becomes a Jacobi, or scalene, ellipsoid (one with all three axes different). Henri Poincaré in 1885...
nearly 4 hours, are expected to be flattened and elongated ellipsoids (Jacobiellipsoids).: 10 To explain Quaoar's non-equilibrium shape, Kiss and collaborators...
onto an ellipsoid in R m . {\displaystyle \mathbf {R} ^{m}.} Non-zero singular values are simply the lengths of the semi-axes of this ellipsoid. Especially...
reference ellipsoid and phase diagrams, as well as the elliptical shape of the Equator, the level spheroid, and the triaxial Jacobiellipsoid. Hopfner...
8 g/cm3 if Huya is a Maclaurin spheroid, and >0.859 g/cm3 if it is a Jacobiellipsoid; however, the occultation found no evidence of an irregular shape for...
includes contributions of Carl Friedrich Gauss (1818), Carl Gustav Jacob Jacobi (1827, 1833/34), Michel Chasles (1829), Victor-Amédée Lebesgue (1837), Thomas...
a quadratic form that defines a surface in the body called Poinsot's ellipsoid. Let Λ {\displaystyle {\boldsymbol {\Lambda }}} be the inertia matrix...
Earth, though many of the underlying principles can be applied to any ellipsoidal geometry. In the original sense, a geodesic was the shortest route between...
the solution set is an ellipsoid or a hyperboloid.[citation needed] If all the eigenvalues are positive, then it is an ellipsoid; if all the eigenvalues...
Hamilton–Jacobi method, in which solutions to Hamilton's equations are sought by first finding a complete solution of the associated Hamilton–Jacobi equation...
Struve, Heinrich von Wild and Moritz von Jacobi, whose theorem has long supported the assumption of an ellipsoid with three unequal axes for the figure...
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