 Conical coordinates

Conical coordinates are a threedimensional orthogonal coordinate system consisting of concentric spheres (described by their radius r) and by two families of perpendicular cones, aligned along the z and xaxes, respectively.
Contents
Basic definitions
The conical coordinates (r,μ,ν) are defined by
with the following limitations on the coordinates
 ν^{2} < c^{2} < μ^{2} < b^{2}
Surfaces of constant r are spheres of that radius centered on the origin
 x^{2} + y^{2} + z^{2} = r^{2}
whereas surfaces of constant μ and ν are mutually perpendicular cones
In this coordinate system, both Laplace's equation and the Helmholtz equation are separable.
Scale factors
The scale factor for the radius r is one (h_{r} = 1), as in spherical coordinates. The scale factors for the two conical coordinates are
References
Bibliography
 Morse PM, Feshbach H (1953). Methods of Theoretical Physics, Part I. New York: McGrawHill. p. 659. ISBN [[Special:BookSources/007043316X, LCCN 5211515007043316X, LCCN 5211515]].
 Margenau H, Murphy GM (1956). The Mathematics of Physics and Chemistry. New York: D. van Nostrand. pp. 183–184. LCCN 5510911.
 Korn GA, Korn TM (1961). Mathematical Handbook for Scientists and Engineers. New York: McGrawHill. p. 179. LCCN 5914456, ASIN B0000CKZX7.
 Sauer R, Szabó I (1967). Mathematische Hilfsmittel des Ingenieurs. New York: Springer Verlag. pp. 991–100. LCCN 6725285.
 Arfken G (1970). Mathematical Methods for Physicists (2nd ed. ed.). Orlando, FL: Academic Press. pp. 118–119. ASIN B000MBRNX4.
 Moon P, Spencer DE (1988). "Conical Coordinates (r, θ, λ)". Field Theory Handbook, Including Coordinate Systems, Differential Equations, and Their Solutions (corrected 2nd ed., 3rd print ed. ed.). New York: SpringerVerlag. pp. 37–40 (Table 1.09). ISBN 9780387184302.
External links
Orthogonal coordinate systems Two dimensional orthogonal coordinate systems Three dimensional orthogonal coordinate systems Cartesian coordinate system • Cylindrical coordinate system • Spherical coordinate system • Parabolic cylindrical coordinates • Paraboloidal coordinates • Oblate spheroidal coordinates • Prolate spheroidal coordinates • Ellipsoidal coordinates • Elliptic cylindrical coordinates • Toroidal coordinates • Bispherical coordinates • Bipolar cylindrical coordinates • Conical coordinates • Flatring cyclide coordinates • Flatdisk cyclide coordinates • Bicyclide coordinates • Capcyclide coordinates • Concave bisinusoidal singlecentered coordinates • Concave bisinusoidal doublecentered coordinates • Convex invertedsinusoidal sphericallyaligned coordinates • Quasirandomintersection cartesian coordinatesCategories: Coordinate systems
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