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A homoeoid is a shell (a bounded region) bounded by two
''Solution nouvelle du problème de l’attraction d’un ellipsoïde hétérogène sur un point exterieur''
Jour. Liouville 5, 465–488 (1840)
A homoeoid is a shell (a bounded region) bounded by two concentric
In geometry, two or more objects are said to be concentric, coaxal, or coaxial when they share the same center or axis. Circles, regular polygons and regular polyhedra, and spheres may be concentric to one another (sharing the same center point ...
, similar ellipse
In mathematics, an ellipse is a plane curve surrounding two focus (geometry), focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special ty ...
s (in 2D) or ellipsoid
An ellipsoid is a surface that may be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation.
An ellipsoid is a quadric surface; that is, a surface that may be defined as the ...
s (in 3D).
When the thickness of the shell becomes negligible, it is called a thin homoeoid. The name homoeoid was coined by Lord Kelvin
William Thomson, 1st Baron Kelvin, (26 June 182417 December 1907) was a British mathematician, Mathematical physics, mathematical physicist and engineer born in Belfast. Professor of Natural Philosophy (Glasgow), Professor of Natural Philoso ...
and Peter Tait Peter Tait may refer to:
* Peter Tait (physicist) (1831–1901), Scottish mathematical physicist
* Peter Tait (footballer) (1936–1990), English professional footballer
* Peter Tait (mayor) (1915–1996), New Zealand politician
* Peter Tait (radio ...
.
Mathematical definition
If the outer shell is given by : with semiaxes the inner shell is given for by :. The thin homoeoid is then given by the limitPhysical meaning
A homoeoid can be used as a construction element of a matter or charge distribution. The gravitational or electromagneticpotential
Potential generally refers to a currently unrealized ability. The term is used in a wide variety of fields, from physics to the social sciences to indicate things that are in a state where they are able to change in ways ranging from the simple re ...
of a homoeoid homogeneously filled with matter or charge is constant inside the shell. This means that a test mass or charge will not feel any force inside the shell.Michel Chasles
Michel Floréal Chasles (; 15 November 1793 – 18 December 1880) was a French mathematician.
Biography
He was born at Épernon in France and studied at the École Polytechnique in Paris under Siméon Denis Poisson. In the War of the Sixth Coali ...
''Solution nouvelle du problème de l’attraction d’un ellipsoïde hétérogène sur un point exterieur''
Jour. Liouville 5, 465–488 (1840)
See also
*Focaloid
In geometry, a focaloid is a shell bounded by two concentric, confocal ellipses (in 2D) or ellipsoids (in 3D). When the thickness of the shell becomes negligible, it is called a thin focaloid.
Mathematical definition (3D)
If one boundary ...
References
External links
* Surfaces Mathematical physics Potentials {{math-physics-stub