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 (AD-688 245), a new system of curvilinear coordinates--hereafter referred to as Roche coordinates was introduced--in 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 three-dimensional 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