ellipsoid of revolution

Then it can be shown that the equipotential solution is an ellipsoid of revolution.

Qualitatively, an egg shape is an ellipsoid of revolution with one end more pointed than the other.

Older literature uses 'spheroid' in place of 'ellipsoid of revolution'.

Thus the next approximation to the true figure of the Earth after the sphere became the oblong ellipsoid of revolution.

They are angles, not metric measures, and describe the direction of the local normal to the reference ellipsoid of revolution.

Modern literature uses the term "ellipsoid of revolution" although the qualifying words "of revolution" are usually dropped.

It is assumed that the rotating Earth is in hydrodynamic equilibrium and is an ellipsoid of revolution.

An ellipsoid which is not an ellipsoid of revolution is called a tri-axial ellipsoid.

If two of the three principal stresses are numerically equal the stress ellipsoid becomes an ellipsoid of revolution.

'Oblate ellipsoid of revolution' is abbreviated to ellipsoid in the remainder of this article.

The surface area of an ellipsoid of revolution (or spheroid) may be expressed in terms of elementary functions:

An ellipsoid of revolution is uniquely defined by two numbers: two dimensions, or one dimension and a number representing the difference between the two dimensions.

When a ellipsoid of revolution (a sphere is a special case) is in contact with a "flat" surface there is a finite area of contact.

C. Niven On the Conduction of Heat in Ellipsoids of Revolution.

An oblate spheroid, or oblate ellipsoid, is an ellipsoid of revolution obtained by rotating an ellipse about its shorter axis.

The shape of an ellipsoid of revolution is determined by the shape of the ellipse which is rotated about its minor (shorter) axis.

Scientific literature (particularly geodesy) often uses 'ellipsoid' in place of 'ellipsoid of revolution' and only applies the adjective 'tri-axial' when treating the general case.

The ultimate goal of his computations was the determination of the precise shape of the Earth, which had long been known to be approximately an ellipsoid of revolution.

Current practice (2012) uses the word 'ellipsoid' alone in preference to the full term 'oblate ellipsoid of revolution' or the older term 'oblate spheroid'.

Flattening is a measure of the compression of a circle or sphere along a diameter to form an ellipse or an ellipsoid of revolution (spheroid) respectively.

Assume the two magnets are ellipsoids of revolution, magnetized along the "long" axes, constrained in a cylindrical tube with N/N or S/S poles.

On the ellipsoid of revolution, geodesics may be written in terms of elliptic integrals, which are usually evaluated in terms of a series expansion; for example, see Vincenty's formulae.

A spheroid, or ellipsoid of revolution is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal (opposing) semi-diameters.

In 1687 Isaac Newton published the Principia in which he included a proof that a rotating self-gravitating fluid body in equilibrium takes the form of an oblate ellipsoid of revolution (a spheroid).

As this vertical is everywhere perpendicular to the idealized surface of mean sea level, or the geoid, this means that the figure of the Earth is even more irregular than an ellipsoid of revolution.