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Elliptic Cylindrical Coordinates

​
xacosh(u) cos(v), yasinh(u) sin(v), zz
u
z
v
a
axes
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
x
-
y
plane are specified, as in the computation of the electric field around an infinite rectangular conducting plate whose intersection with the
x
-
y
plane is the line segment with endpoints
(-a,0)
and
(a,0)
.
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