Topic
Elliptic coordinate system
About: Elliptic coordinate system is a research topic. Over the lifetime, 670 publications have been published within this topic receiving 11135 citations. The topic is also known as: elliptical coordinate system & elliptic coordinates.
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01 Jan 1934
TL;DR: The mathematical treatment of these coordinates is simplified by their symmetry as discussed by the authors, and the equation of definition between the elliptical coordinates λ, μ and v and the Cartesian coordinates x, y, and z is one and the same for all three of them.
Abstract: The motion of a perfect fluid at rest except for the effect of the translation of an ellipsoid with three unequal axes is studied by means of elliptic coordinates. The mathematical treatment of these coordinates is simplified by their symmetry. The equation of definition between the elliptical coordinates λ, μ and v and the Cartesian coordinates x, y, and z is one and the same for all three of them. This does not mean that the three elliptical coordinates at each point have the same value. They have different values, the equation defining them being of the third degree and possessing three different roots, one for each elliptical coordinate.
1 citations
TL;DR: In this article, a study of the hydrogen molecular ion (H2+), confined strongly in two dimensions by ellipses of different sizes ξ0, is done, where the Schrodinger equation is solved numerically in elliptic coordinates (ξ, η), applying the separation of variables method.
1 citations
Journal Article•
TL;DR: In this article, a series of adaptive corrdinate transformation methods are proposed in which the grid angles are preserved approximately, and the material interface is kept to be Lagrangian description and a minimum difference (in the least-squares sense) between the mesh velocity and the fluid velocity is achieved.
Abstract: A series of adaptive corrdinate transformation methods are proposed in which the grid angles are preserved approximately, and the material interface is kept to be Lagrangian description and a minimum difference (in the least-squares sense) between the mesh velocity and the fluid velocity is achieved. The new coordinate system is adapted to important features of flow fields.
1 citations
01 Jan 1999
1 citations
TL;DR: In this paper, an analytical examination of electromagnetic boundary conditions at the interface between two different media is presented in an orthogonal curvilinear coordinate system which conforms locally and instantaneously to the interface.
Abstract: In Part I, an analytical examination of electromagnetic boundary conditions at the interface between two different media is presented in an orthogonal curvilinear coordinate system which conforms locally and instantaneously to the interface. Subsequently, an original natural coordinate system is introduced to resolve the uncertainty in the choice of an orthogonal curvilinear coordinate system. This natural coordinate system is also appeared to reduce the number of the nonvanishing discontinuity relations, and to determine local and instantaneous natural aspects of the e.m. boundary conditions problem.
1 citations