Homoeoid

A Homöoid is in three dimensions, a shell, which is bounded by two concentric, like ellipsoids. In two dimensions a Homöoid is an elliptical ring, which is bounded by respective ellipses.

Mathematical definition

If the outer boundary by an implicitly given ellipsoid

Described with the semi-axes, then for the inner boundary by

Given.

In the limiting case of one speaks of thin, in the other case of thick Homöoiden.

Physical Meaning I

The physical meaning of the Homöoiden potential theory is that within a homogeneously filled with ground or charge Homöoiden a test mass charge or no force is applied, that is, the corresponding potential is constant. This does not apply to other elliptical shells ( for example: Fokaloide ). The potential in the exterior of a thin Homöoiden is constant on ellipsoids that are confocal to this Homöoiden. These remarkable properties have already been demonstrated by Isaac Newton.

Definition homöoidale distribution

One speaks of a homöoidalen density distribution when the layers of constant density of a mass or charge distribution are given by concentric ellipsoids similar to each other.

Physical Meaning II

Within a homöoidalen density distribution contribute to the force acting on a body only the layers that are located within the boundary of concentric, similar ellipsoids, which runs through the body.