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.

Pure Bending of Elliptical Ring Sector with Cross Section of Multi-Connected Region Composed of Confocal Ellipses

Abstract: In this study, internal stresses of an elliptical ring sector with the cross section of a multi connected region composed of two confocal ellipses, subjected to pure bending are analyzed. Gohner's method is used for analysis and therefore, some difficulties caused by elliptical coordinates are eliminated. The analysis is limited to determining the first correction to the initial stress state for pure bending of an elliptical ring sector with the cross section of two confocal ellipses.

Map Projections and Local Coordinate Systems

Abstract: Coordinate systems are an integral part of modern surveying and geomatics. This chapter focuses primarily on georeferenced coordinate systems, or spatial reference systems, which range in extent from global to local. When a map projection is associated with a specific geodetic datum, it is called a projected coordinate system (PCS). State plane coordinate systems are multizone systems of conformal PCSs in which each zone is designed using transverse mercator, lambert conformal conic, or Hotine oblique mercator projections. Map projection linear distortion is manifested as a difference in distance between a pair of projected coordinates and the true horizontal distance at the surface of the Earth. Also explored are large-scale conformal projected coordinate systems for surveying engineering, which became common in the United States after the creation of the State Plane Coordinate System in the 1930s by the National Geodetic Survey.

Analytical approach for resolving stress states around elliptical cavities

Abstract: The determination of stress states around cavities in the stressed elastic body, regardless of cavity shapes, that may be spherical, cylindrical elliptical etc. in its analytical approach has to be based on selection of a stress function that will satisfy biharmonic equation, under given boundary conditions. This paper is concerned with formulation and solution of the cited differential equation using elliptical coordinates in conformity with the cavity shape of oblong ellipsoid [1]. It is therefore considered that the formulation of the stress tensor will be done in conformity to the cited coordinates. The paper describes basic statements and definitions in connection to harmonic functions used for determination of stress states around cavities formed in the stressed homogeneous space. The particular attention has been paid to the use of Legendre`s functions, with definitions and derivation of recurrent formulas, that have been used for determination of stress states around an oblong ellipsoidal cavity, [1]. The paper also includes the description of procedures used in forming series based on Legendre`s functions of the first order.

Integrable Systems and Confocal Quadrics

Abstract: A family of confocal quadrics in a projective space and the elliptic coordinates associated with these quadrics are known to be a powerful tool for explicit solving various integrable systems in terms of the Abelian integrals. Using the elliptic coordinates associated with such quadrics K. Jacobi solved the problem on the geodesics on an ellipsoid and K. Neumann [9] did the same for the problem of a mass point motion on a sphere in a force field with a quadratic potential.