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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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 paper, it was shown that the Hamilton-Jacobi equation for massless geodesics can only separate in elliptic or spherical coordinates, and all known integrable backgrounds are covered by this separation.
Abstract: Motivated by the search for new backgrounds with integrable string theories, we classify the D-brane geometries leading to integrable geodesics. Our analysis demonstrates that the Hamilton-Jacobi equation for massless geodesics can only separate in elliptic or spherical coordinates, and all known integrable backgrounds are covered by this separation. In particular, we identify the standard parameterization of AdSp × Sq with elliptic coordinates on a flat base. We also find new geometries admitting separation of the Hamilton-Jacobi equation in the elliptic coordinates. Since separability of this equation is a necessary condition for integrability of strings, our analysis gives severe restrictions on the potential candidates for integrable string theories.
78 citations
TL;DR: The representation of electromagnetic quantities by differential forms allows the use of nonorthogonal coordinate systems as mentioned in this paper, and a judicious choice of coordinate system facilitates the finite element modeling of infinite or very thin domains.
Abstract: The representation of electromagnetic quantities by differential forms allows the use of nonorthogonal coordinate systems. A judicious choice of coordinate system facilitates the finite element modeling of infinite or very thin domains.
73 citations
TL;DR: In this paper, the authors derive interpolation formulae for a third-order finite difference method in curvilinear, orthogonal coordinate systems, which serve as a supplement to Colella and Woodward's PPM scheme for problems where the coordinate origin is included in the computational domain.
Abstract: We derive interpolation formulae for a third-order finite difference method in curvilinear, orthogonal coordinate systems. These formulae serve as a supplement to Colella and Woodward's PPM scheme for problems where the coordinate origin is included in the computational domain. Numerical examples of the improved accuracy of the advection scheme near coordinate singularities are shown.
68 citations