Parabolic Coordinates

A system of Curvilinear Coordinates in which two sets of coordinate surfaces are obtained by revolving the parabolasof Parabolic Cylindrical Coordinates about the x-Axis, which is then relabeled the z-Axis. Thereare several notational conventions. Whereas is used in this work, Arfken (1970) uses .

The equations for the parabolic coordinates are

			(1)
			(2)
			(3)

			(4)

(5)

(6)

(7)

			(8)
			(9)
			(10)

			(11)
			(12)
			(13)

(14)

(15)

			(16)

References

Arfken, G. ``Parabolic Coordinates (, , ).'' §2.12 in Mathematical Methods for Physicists, 2nd ed. Orlando, FL: Academic Press, pp. 109-112, 1970.

Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, p. 660, 1953.

• Donaldson Invariants
• Donkin's Theorem
• Donut
• Doob's Theorem
• Dot
• Dot Product
• Variate
• Variation
• Variation Coefficient
• Variation of Argument
• Variation of Parameters
• Variety
• Varignon Parallelogram
• Varignon's Theorem
• Vassiliev Polynomial
• Vault
• Vector
• Vector Bundle
• Vector Derivative
• Vector Direct Product
• Vector Division
• Vector Field
• Vector Function
• Vector Harmonic
• Vector Integral