Ellipsoid With Three Unequal Axes

Abstract

The motion of a perfect fluid at rest except for the effect of the translation of an ellipsoid with three unequal axes is studied by means of elliptic coordinates. The mathematical treatment of these coordinates is simplified by their symmetry. The equation of definition between the elliptical coordinates λ, μ and v and the Cartesian coordinates x, y, and z is one and the same for all three of them. This does not mean that the three elliptical coordinates at each point have the same value. They have different values, the equation defining them being of the third degree and possessing three different roots, one for each elliptical coordinate.