Accession Number : AD0688245

Title :   THE ROCHE COORDINATES AND THEIR USE IN CELESTIAL MECHANICS OR HYDRODYNAMICS,

Corporate Author : BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH MATHEMATICS RESEARCH LAB

Personal Author(s) : Kopal,Zdenek

Report Date : APR 1969

Pagination or Media Count : 52

Abstract : The air of the report will be to introduce a new system of curvilinear coordinates--hereafter referred to as Roche coordinates--in which spheres of constant radius are replaced by equipotential surfaces of a rotating gravitational dipole (which consists of two discrete points of finite mass, revolving around their common center of gravity); while the remaining coordinates are orthogonal to the equipotentials. It will be shown that the use of such coordinates offers a new method of approach to the solution of certain problems of particle dynamics (such as, for instance, the construction of certain types of trajectories in the restricted problem of three bodies); as well as of the hydrodynamics of gas streams in close binary systems, in which the equipotential surfaces of their components distorted by axial rotation and mutual tidal interaction constitute essential boundary conditions. (Author)

Descriptors :   (*N-BODY PROBLEM, TRANSFORMATIONS(MATHEMATICS)), (*HYDRODYNAMICS, EQUATIONS), POTENTIAL THEORY, EQUATIONS OF MOTION, GRAVITY, DIFFERENTIAL EQUATIONS, GEOMETRY

Subject Categories : Celestial Mechanics
      Fluid Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE