The coordinates are the asymptotic angle of confocal Parabola segments symmetrical about the axis. The
coordinates are confocal Ellipses centered on the origin.
(1) | |||
(2) | |||
(3) |
(4) |
(5) |
(6) | |||
(7) | |||
(8) | |||
(9) | |||
(10) | |||
(11) | |||
(12) |
(13) |
(14) | |||
(15) | |||
(16) |
(17) | |||
(18) | |||
(19) |
See also Cylindrical Coordinates, Helmholtz Differential Equation--Elliptic Cylindrical Coordinates
References
Arfken, G. ``Elliptic Cylindrical Coordinates (, , ).'' §2.7 in
Mathematical Methods for Physicists, 2nd ed. Orlando, FL: Academic Press, pp. 95-97, 1970.
Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, p. 657, 1953.
© 1996-9 Eric W. Weisstein