Homoeoid

A homoeoid is a shell (a bounded region) bounded by two concentric, similar ellipses (in 2D) or ellipsoids (in 3D).[1][2] 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.[3]

Cut view of a homoeoid in 3D

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 limit

Physical meaning

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.[4]

gollark: I managed to hack into the global financial system by typing very fast with a terminal open, so now I have money for a domain. osmarksdomain™ *is* inevitable.
gollark: Great!
gollark: Hi.
gollark: Coral Shoe Transfer Protocol when?
gollark: Apiohypnoforms inbound.

See also

References
  1. Chandrasekhar, S.: Ellipsoidal Figures of Equilibrium, Yale Univ. Press. London (1969)
  2. Routh, E. J.: A Treatise on Analytical Statics, Vol II, Cambridge University Press, Cambridge (1882)
  3. Harry Bateman. "Partial differential equations of mathematical physics.", Cambridge, UK: Cambridge University Press, 1932 (1932).
  4. 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
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.