Homoeoid

Homoeoid in 3D

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.

Mathematical definition

If the outer shell is given by


\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1

with semiaxes a,b,c the inner shell is given for 0 \leq m \leq 1 by


\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=m^2
.

The thin homoeoid is then given by the limit 
m \to 1

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.

References

See also

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