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Elliptic Cylindrical Coordinates


	The elliptic cylindrical curvilinear coordinate system is one of the many coordinate systems that make the Laplace and Helmoltz differential equations separable. This system is used when simple boundary conditions on a segment in the - plane are specified, as in the computation of the electric field around an infinite rectangular conducting plate whose intersection with the - plane is the line segment with endpoints and .


	Contributed by: Adriano Pascoletti
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The more opaque half of the hyperbolic cylinder has

; the other half has

From the tutorial on Mathematica Vector Analysis Package: The elliptic cylindrical coordinate system

, parameterized by

, is built around two foci separated by

. Holding coordinate

constant while varying the other coordinates produces a family of confocal ellipses. Fixing coordinate

produces a family of confocal hyperbolas. The coordinate

specifies distance along the axis of common focus. The default value for parameter

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