Other differential operators such as and can be expressed in the coordinates by substituting the scale factors into the general formulae found in orthogonal coordinates.
Angular parametrizationedit
An alternative parametrization exists that closely follows the angular parametrization of spherical coordinates:[1]
Here, parametrizes the concentric ellipsoids around the origin and and are the usual polar and azimuthal angles of spherical coordinates, respectively. The corresponding volume element is
Morse PM, Feshbach H (1953). Methods of Theoretical Physics, Part I. New York: McGraw-Hill. p. 663.
Zwillinger D (1992). Handbook of Integration. Boston, MA: Jones and Bartlett. p. 114. ISBN 0-86720-293-9.
Sauer R, Szabó I (1967). Mathematische Hilfsmittel des Ingenieurs. New York: Springer Verlag. pp. 101–102. LCCN 67025285.
Korn GA, Korn TM (1961). Mathematical Handbook for Scientists and Engineers. New York: McGraw-Hill. p. 176. LCCN 59014456.
Margenau H, Murphy GM (1956). The Mathematics of Physics and Chemistry. New York: D. van Nostrand. pp. 178–180. LCCN 55010911.
Moon PH, Spencer DE (1988). "Ellipsoidal Coordinates (η, θ, λ)". Field Theory Handbook, Including Coordinate Systems, Differential Equations, and Their Solutions (corrected 2nd, 3rd print ed.). New York: Springer Verlag. pp. 40–44 (Table 1.10). ISBN 0-387-02732-7.
Unusual conventionedit
Landau LD, Lifshitz EM, Pitaevskii LP (1984). Electrodynamics of Continuous Media (Volume 8 of the Course of Theoretical Physics) (2nd ed.). New York: Pergamon Press. pp. 19–29. ISBN 978-0-7506-2634-7. Uses (ξ, η, ζ) coordinates that have the units of distance squared.
External linksedit
MathWorld description of confocal ellipsoidal coordinates