Showing papers on "Elliptic coordinate system published in 1974"
TL;DR: In this paper, a method for automatic numerical generation of a general curvilinear coordinate system with coordinate lines coincident with all boundaries of general multi-connected regions containing any number of arbitrarily shaped bodies is presented.
996 citations
TL;DR: In this article, a method of writing the conservation equations of gasdynamics in curvilinear coordinates which eliminates undifferentiated terms is presented. But the method is only applicable to orthogonal coordinates and not to general tensor transformations.
427 citations
TL;DR: In this article, the authors presented numerical solutions for stresses around an elliptical hole in a long, thin, circular cylindrical shell subjected to axial tension for both the symmetric orientations of the hole with respect to the shell.
20 citations
TL;DR: In this paper, an alternative method to that of Cheshire is presented for evaluating exchange matrix elements of the types occurring in close coupling-based treatments of ion-atom scattering, which consists in reducing by quadrature the matrix elements (which are expressible as two dimensional integrals in confocal elliptic coordinates) to one dimension integrals which are then numerically calculated via Gauss-Laguerre quadratures.
Abstract: An alternative method to that of Cheshire is presented for evaluating exchange matrix elements of the types occurring in close coupling-based treatments of ion-atom scattering. The idea consists in reducing by quadrature the matrix elements (which are expressible as two dimensional integrals in confocal elliptic coordinates) to one dimensional integrals which are then numerically calculated via Gauss-Laguerre quadrature. The scheme which has been tested in both the two-state and three-state approximations represents a considerable saving in computing time. This should enable one to subject to practical test the important question of the rate of convergence of close coupling-type expansions in these problems.
8 citations
TL;DR: In this article, a non-Galilean coordinate system was used to solve the problem of the electromagnetic field of a charge executing hyperbolic motion in the presence of an electric field.
Abstract: A method based on the use of non-Galilean coordinate systems is discussed for solving certain problems of electrodynamics. The method is used to solve the problem of the electromagnetic field of a charge executing hyperbolic motion.