Eccentric Dipole Coordinates

A note on the dipole coordinates

by, for example, a finite difference method in the computational (μ, χ, φ) space. The above standard dipole coordinates is convenient and certainly appropriate for analytical studies in which the Earth’s dipolar field plays central roles. It also works as a base coordinates for the node and cell generation of the finite element method in the dipole geometry [2, 3]. However, when one tries to us...

The electric field of an eccentric dipole in a homogeneous spherical conducting medium.

The electrical position of the heart with reference to the electrodes used in studying its field is unknown. For reasons presented. it is more likely eccentric; hence, the equation defining the field of an eccentric dipole in a spherical medium might be useful for projected experimental studies and for better understanding of the way in which a given electrical position determines the electrode...

Eccentric Behavior of Eccentric Planets

Recent increases in the discovery of high multiplicity Sub-Jovian planetary systems, in addition to discoveries of giant planets of high eccentricities in these multiple body systems, lead to questions into their origins and evolution. The study of secular interactions is not new, however it has only recently been applied to exoplanetary systems. These systems sometimes fall far from the classi...

Electric-dipole matrix-element formulas in hyperspherical coordinates with applications to H- and He.

Transforming Geocentric Cartesian Coordinates to Geodetic Coordinates by a New Initial Value Calculation Paradigm

Transforming geocentric Cartesian coordinates (X, Y, Z) to geodetic curvilinear coordinates (φ, λ, h) on a biaxial ellipsoid is one of the problems used in satellite positioning, coordinates conversion between reference systems, astronomy and geodetic calculations. For this purpose, various methods including Closed-form, Vector method and Fixed-point method have been developed. In this paper, a...