Derivation of the Clairaut integrodifferential equation by the Pizzetti method

Details Derivation of the Clairaut integrodifferential equation by the Pizzetti method Derivation of the Clairaut integrodifferential equation by the Pizzetti method

Dec 1990

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990kfnt....6...73o&link_type=abstract

Kinematika i Fizika Nebesnykh Tel (ISSN 0233-7665), vol. 6, Nov.-Dec. 1990, p. 73-78. In Russian.

Physics

Differential Equations, Geoids, Gravitational Effects, Integral Equations, Rotating Fluids, Bodies Of Revolution, Ellipsoids, Equilibrium Methods

Scientific paper

A system of several different equations is derived from the combined solution of the functional Pizzetti equation and the equation of the supposed equilibrium figure of a rotating gravitizing liquid mass. It is shown that, when applied to Clairaut's hypothesis that the earth's figure is an ellipsoid of rotation, the Pizzetti method yields a family of four equations, one of which is the well-known Clairaut integrodifferential equation.

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