Derivation of the Clairaut integrodifferential equation by the Pizzetti method.
Abstract
Combined solution of the functional Pizzetti equation and the equation of the supposed equilibrium figure of a rotating gravitating liquid mass leads to a system of several differential equations. It is shown that Pizzetti's method as applied to the Clairaut hypothesis on the Earth's figure as an ellipsoid of rotation presents a family of four equations one of which is the wellknown Clairaut integrodifferential equation. Its solution is given.
 Publication:

Kinematika i Fizika Nebesnykh Tel
 Pub Date:
 December 1990
 Bibcode:
 1990KFNT....6...73O
 Keywords:

 Differential Equations;
 Geoids;
 Gravitational Effects;
 Integral Equations;
 Rotating Fluids;
 Bodies Of Revolution;
 Ellipsoids;
 Equilibrium Methods;
 Geophysics;
 Earth: Figure