Third-Order Clairaut Equation for a Rotating Body of Arbitrary Density and Its Application to Marine Geodesy.
NAVAL RESEARCH LAB WASHINGTON D C
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This report derives the Clairaut equations, which govern the deformation of the equipotential surfaces within a rotating mass in hydrostatic equilibrium, as ordinary differential equations containing up to third-order terms in a small parameter. This has been achieved by a eliminating the two integral terms which appeared in the original formulation, and b by expanding the equipotential surfaces into a power series of a small parameter which is essentially the ratio between the rotational and potential energy of the body.