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Two-center bipolar coordinates
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Two-center bipolar coordinates : ウィキペディア英語版
Two-center bipolar coordinates
:''For related concepts, see Bipolar coordinates.''
In mathematics, two-center bipolar coordinates is a coordinate system, based on two coordinates which give distances from two fixed centers, c_1 and c_2. This system is very useful in some scientific applications (e.g. calculating the electric field of a dipole on a plane).〔(R. Price, The Periodic Standing Wave Approximation: Adapted coordinates and spectral methods. )〕〔(The periodic standing-wave approximation: nonlinear scalar fields, adapted coordinates, and the eigenspectral method. )〕
==Transformation to Cartesian coordinates==

The transformation to Cartesian coordinates (x,\ y) from two-center bipolar coordinates (r_1,\ r_2) is
:
x = \frac

:
y = \pm \frac\sqrt

where the centers of this coordinate system are at (+a,\ 0) and (-a,\ 0).〔

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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