A homoeoid is a shell (a bounded region) bounded by two concentric, similar ellipses (in 2D) or ellipsoids (in 3D). When the thickness of the shell becomes negligible, it is called a thin homoeoid. The name homoeoid was coined by Lord Kelvin and Peter Tait.
If the outer shell is given by
with semiaxes the inner shell is given for by
The thin homoeoid is then given by the limit
A homoeoid can be used as a construction element of a matter or charge distribution. The gravitational or electromagnetic potential 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.
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- Routh, E. J.: A Treatise on Analytical Statics, Vol II, Cambridge University Press, Cambridge (1882)
- Harry Bateman. "Partial differential equations of mathematical physics.", Cambridge, UK: Cambridge University Press, 1932 (1932).
- Michel Chasles, Solution nouvelle du problème de l’attraction d’un ellipsoïde hétérogène sur un point exterieur, Jour. Liouville 5, 465–488 (1840)
- Media related to Homoeoid at Wikimedia Commons