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Bispherical coordinates
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Bispherical coordinates : ウィキペディア英語版
Bispherical coordinates

Bispherical coordinates are a three-dimensional orthogonal coordinate system that results from rotating the two-dimensional bipolar coordinate system about the axis that connects the two foci. Thus, the two foci F_ and F_ in bipolar coordinates remain points (on the z-axis, the axis of rotation) in the bispherical coordinate system.
==Definition==
The most common definition of bispherical coordinates (\sigma, \tau, \phi) is
:
x = a \ \frac \cos \phi

:
y = a \ \frac \sin \phi

:
z = a \ \frac

where the \sigma coordinate of a point P equals the angle F_ P F_ and the \tau coordinate equals the natural logarithm of the ratio of the distances d_ and d_ to the foci
:
\tau = \ln \frac}


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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