Showing papers on "Elliptic coordinate system published in 1985"
TL;DR: In this article, a finite-difference algorithm for recirculating flow problem in a body-fitted coordinate system is presented, where a fully staggered grid system is adopted for the velocity components and the scalar variables.
Abstract: A finite-difference algorithm for recirculating flow problem! in a body-fitted coordinate system is presented. A fully staggered grid system is adopted for the velocity components and the scalar variables. The strong conservation law form of the governing equations is written in the general curvilinear coordinates. The SIMPLE calculation procedure originally developed in Cartesian coordinates is extended to the present curvilinear coordinates. Two methods of evaluating the metric derivatives are discussed. Although both methods are formally of the same order of accuracy, it is shown that one performs the physical conservation laws more accurately than the other. The relative merits of three schemes, i.e., hybrid, second-order upwinding, and QUICK, for approximating the convection terms in the momentum equations are compared and the results are quite different from those in Cartesian coordinates in both accuracy and efficiency aspects. The effects of the grid distribution are also studied. Results obtained...
191 citations
TL;DR: In this paper, it was shown that the Hamiltonian (1.1) has n functionally independent integrals of motion in involution which are rational both in phase space variables and in parameters.
Abstract: We show here that the Hamiltonian (1.1) has n functionally independent integrals of motion in involution which are rational both in phase space variables and in parameters. Moreover these integrals are quadratic in momenta and the Hamilton-Jacobi equation of the system (1.1) is separable in generalized elliptic coordinates. A Lax representation for (1.1) and for higher flows is found. The system (1.1) constrained to an ellipsoid remains integrable.
85 citations
TL;DR: In this article, two families of elementary one-particle potentials of n degrees of freedom which are separable in elliptical-spherical coordinates or in generalized elliptic coordinates were found.
55 citations
30 citations
TL;DR: In this paper, the direct transformation of the Cartesian coordinate system into a system of geodetic coordinates is discussed, and relations for direct transformation from Cartesian coordinates to geodetectors are established.
Abstract: Relations for the direct transformation of the Cartesian coordinate system into a system of geodetic coordinates.
25 citations
TL;DR: In this article, the authors used the method of spectral series expansion to reduce the governing coupled partial differential equations to three sets of second-order ordinary equations and then numerically integrated using COLSYS, a finite-element collocation code for boundary value differential equations.
22 citations
TL;DR: In this article, the exact solutions of the covariant generalization of the Dirac equation are obtained in the Kasner space-time for two types of coordinates, cartesian coordinates and cylindrical ones.
15 citations
5 citations
TL;DR: In this article, a coordinate-free exposition of the theory of multidimensional Jacobi coordinates, which are used to integrate the equations of geodesics on an ellipsoid as well as other equations, is given.
Abstract: A coordinate-free exposition of the theory of multidimensional Jacobi coordinates, which are used to integrate the equations of geodesics on an ellipsoid as well as other equations, is given. Generalizations of the theorems of Newton and Ivory, concerning the attraction field produced by an ellipsoid, are given.
1 citations