THE ROCHE COORDINATES IN THREE DIMENSIONS AND THEIR APPLICATION TO HYDRODYNAMICS,

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)

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1969
Accession Number
AD0694496

Entities

People

  • Zdenek Kopal

Organizations

  • Boeing

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Equations
  • Fluid Dynamics
  • Fluid Mechanics
  • Geometry
  • Hydrodynamics
  • Mathematics
  • Mechanics
  • Three Dimensional

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Graph Algorithms and Convex Optimization.
  • Plasma Physics / Magnetohydrodynamics