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.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this article, a complete double wave function description for space rotator systems in Cartesian coordinate is given, and the classical mechanical time evolution equations are found as the classical limit case of the evolution equations.
Abstract: In this paper, a complete, so-called double wave function description for space rotator systems in Cartesian coordinate is given. The time evolution equation for every observable in the coordinate is presented. The classical mechanical time evolution equations are found as the classical limit case of the evolution equations. And the conventional quantum mechanical description is yielded in two equivalent statistical cases. Our studies show that the Cartesian coordinate offers more perfect description than the spherical polar one does.
1 citations
01 May 2012
TL;DR: In this article, a particle motion analysis when a problem becomes integrable in the normalized polar coordinates is presented, which yields an exact analytical solution and has a uniform longitudinal coordinate dependence of the fields since the corresponding nonlinear potential is invariant under the transformation from the Cartesian to the normalized coordinates.
Abstract: Several families of nonlinear accelerator lattices with integrable transverse motion were suggested recently. One of the requirements for the existence of two analytic invariants is a special longitudinal coordinate dependence of fields. This paper presents the particle motion analysis when a problem becomes integrable in the normalized polar coordinates. This case is distinguished from the others: it yields an exact analytical solution and has a uniform longitudinal coordinate dependence of the fields (since the corresponding nonlinear potential is invariant under the transformation from the Cartesian to the normalized coordinates). A number of interesting features are revealed: while the frequency of radial oscillations is independent of the amplitude, the spread of angular frequencies in a beam is absolute. A corresponding spread of frequencies of oscillations in the Cartesian coordinates is evaluated via the simulation of transverse Schottky noise.
1 citations
01 Jan 2016
TL;DR: In this paper, the authors present the curvilinear coordinates that they use for describing a shallow mass flow down arbitrary topography, and present a model for the description of such a flow.
Abstract: This chapter is devoted to the presentation of the curvilinear coordinates that we use for the description of a shallow mass flow down arbitrary topography.
1 citations
Journal Article•
1 citations