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If the three axes have different lengths, the figure is a triaxial ellipsoid (rarely scalene ellipsoid), and the axes are uniquely defined. If two of the axes have the same length, then the ellipsoid is an ellipsoid of revolution , also called a spheroid .
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 .
Scalene may refer to: A scalene triangle, one in which all sides and angles are not the same. A scalene ellipsoid, one in which the lengths of all three semi-principal axes are different; Scalene muscles of the neck; Scalene tubercle, a slight ridge on the first rib prolonged internally into a tubercle
In geophysics, geodesy, and related areas, the word 'ellipsoid' is understood to mean 'oblate ellipsoid of revolution', and the older term 'oblate spheroid' is hardly used. [2] [3] For bodies that cannot be well approximated by an ellipsoid of revolution a triaxial (or scalene) ellipsoid is used.
An alternative parametrization exists that closely follows the angular parametrization of spherical coordinates: [1] = , = , = . Here, > parametrizes the concentric ellipsoids around the origin and [,] and [,] are the usual polar and azimuthal angles of spherical coordinates, respectively.
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However, in the cases of moons in synchronous orbit, nearly unidirectional tidal forces create a scalene ellipsoid. Also, the purported dwarf planet Haumea is scalene because of its rapid rotation though it may not currently be in equilibrium. Icy objects were previously believed to need less mass to attain hydrostatic equilibrium than rocky ...
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