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 Dec 1956
TL;DR: In this paper, the theory of thin shallow shells is discussed. But the authors do not employ the lines of curvature as the coordinate system, but employ "almost cartesian coordinates" or the coordinates obtained by cutting the surface into two mutually orthogonal systems of parallel planes.
Abstract: This report is concerned with the theory of thin shallow shells. It does not employ the lines of curvature as the coordinate system, but employs "almost cartesian coordinates" or the coordinates obtained by cutting the surface into two mutually orthogonal systems of parallel planes.
3 citations
TL;DR: In this paper, the free vibration frequencies of finite-length simply-supported elastic elliptical cylinders were determined in an exact manner using the Helmholtz decomposition theorem and the classical technique of separation of variables in elliptical coordinates.
3 citations
TL;DR: In this article, it was shown that only one of the two sets gives the conventional interpretation of quantum field theory, based on a Fock space, and discarding the other set, one can still keep the Milne coordinate system.
Abstract: The upper and lower quadrants of flat space-time can be described using the Milne coordinate system. The Klein-Gordon equation of a scalar field in such a coordinate system admits at least two sets of solutions. Based on the Feynman propagator behavior it is shown that only one of the two sets gives the conventional interpretation of quantum field theory, based on a Fock space. Therefore, discarding the other set, one can still keep the Milne coordinate system.
3 citations
TL;DR: In this paper, a system of two equations is developed that allows the time evolution of the underwater spark channel to be calculated numerically from a given power input, and the proposed mathematical model utilizes the elliptical coordinates.
Abstract: In this study, a system of two equations is developed that allows the time evolution of the underwater spark channel to be calculated numerically from a given power input. The proposed mathematical model utilizes the elliptical coordinates. This approach has the advantage of considering the underwater spark as an expanding ellipsoid, which closely corresponds to experimental observations. Similar to spherical or cylindrical models, the proposed method considers only one spatial coordinate as a function of time, which simplifies the analysis. The predictions of this model are compared with the experimental results.
3 citations
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TL;DR: In this paper, the integrable Camassa-Holm equation on the line with positive initial data rapidly decaying at infinity was considered and a one parameter family of integrably hierarchies which preserves the mixed spectrum of the associated string spectral problem was constructed.
Abstract: We consider the integrable Camassa--Holm equation on the line with positive initial data rapidly decaying at infinity. On such phase space we construct a one parameter family of integrable hierarchies which preserves the mixed spectrum of the associated string spectral problem. This family includes the CH hierarchy. We demonstrate that the constructed flows can be interpreted as Hamiltonian flows on the space of Weyl functions of the associated string spectral problem. The corresponding Poisson bracket is the Atiyah--Hitchin bracket. Using an infinite dimensional version of the Jacobi ellipsoidal coordinates we obtain a one parameter family of canonical coordinates linearizing the flows.
3 citations