
Accession Number : AD0694496
Title : THE ROCHE COORDINATES IN THREE DIMENSIONS AND THEIR APPLICATION TO HYDRODYNAMICS,
Corporate Author : BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH MATHEMATICS RESEARCH LAB
Personal Author(s) : Kopal,Zdenek
Report Date : SEP 1969
Pagination or Media Count : 34
Abstract : In a preceding report (AD688 245), a new system of curvilinear coordinateshereafter referred to as Roche coordinates was introducedin which spheres of constant radius are replaced by equipotential surfaces of a rotating gravitational dipole, while the remaining angular coordinates are made orthogonal to the equipotentials. In the previous report the explicit form of such coordinates was derived, and their relationship was established with polar coordinates (with which they coalesce in the immediate neighborhood of each one of the two mass points) in the plane case. The aim of the present report will be to generalize the definition of the Roche coordinates to three dimensions. A formulation of the fundamental equations of hydrodynamics is given in terms of threedimensional Roche coordinates; and their advantages for treatment of certain classes of dynamical problems are illustrated. (Author)
Descriptors : (*HYDRODYNAMICS, EQUATIONS OF MOTION), CELESTIAL MECHANICS, TRANSFORMATIONS(MATHEMATICS), POTENTIAL THEORY, PARTIAL DIFFERENTIAL EQUATIONS, GEOMETRY
Subject Categories : Theoretical Mathematics
Fluid Mechanics
Distribution Statement : APPROVED FOR PUBLIC RELEASE