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

Conical coordinates are a three-dimensional orthogonal coordinate system consisting of
concentric spheres (described by their radius r) and by two families of perpendicular cones, aligned along the ''z''- and ''x''-axes, respectively.
==Basic definitions==

The conical coordinates (r, \mu, \nu) are defined by
:
x = \frac

:
y = \frac \sqrt \right) \left( \nu^ - b^ \right)} \right)} }

:
z = \frac \sqrt \right) \left( \nu^ - c^ \right)} \right)} }

with the following limitations on the coordinates
:
\nu^ < c^ < \mu^ < b^

Surfaces of constant r are spheres of that radius centered on the origin
:
x^ + y^ + z^ = r^

whereas surfaces of constant \mu and \nu are mutually perpendicular cones
:
\frac} + \frac + b^} + \frac - c^} = 0

:
\frac} + \frac - b^} + \frac + c^} = 0

In this coordinate system, both Laplace's equation and the Helmholtz equation are separable.

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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