A general system of fourth-order curvilinear coordinates based on the cyclide in which Laplace's
equation is separable (either simply
separable or 
-separable).
Bôcher (1894) treated all possible systems of this class (Moon and Spencer
1988, p. 49).
Cyclidic Coordinates
See also
Bicyclide Coordinates, Cap-Cyclide Coordinates, Disk-Cyclide Coordinates, Orthogonal Coordinate SystemExplore with Wolfram|Alpha
References
Bôcher, M. Über die Reihenentwicklungen der Potentialtheorie. Leipzig, Germany: Teubner, 1894.Byerly, W. E. An Elementary Treatise on Fourier's Series, and Spherical, Cylindrical, and Ellipsoidal Harmonics, with Applications to Problems in Mathematical Physics. New York: Dover, p. 273, 1959.Casey, J. "On Cyclides and Sphero-Quartics." Philos. Trans. Roy. Soc. London 161, 585-721, 1871.Darboux, G. "Remarques sur la théorie des surfaces orthogonales." Comptes Rendus Acad. Sci. Paris 59, 240-242, 1864.Darboux, G. "Sur l'application des méthodes de la physique mathématique à l'étude de corps terminés par des cyclides." Comptes Rendus Acad. Sci. Paris 83, 1037-1039, 1864.Klein, F. Über lineare Differentialgleichungen der zweiter Ordnung; Vorlesungen gehalten im Sommersemester 1894. Göttingen, Germany: 1894.Maxwell, J. C. "On the Cyclide." Quart. J. Pure Appl. Math. 9, 111-126, 1868.Moon, P. and Spencer, D. E. Field Theory Handbook, Including Coordinate Systems, Differential Equations, and Their Solutions, 2nd ed. New York: Springer-Verlag, 1988.Wangerin. Preisschriften der Jablanowski'schen Gesellschaft, No. 18, 1875-1876.Wangerin. Crelle's J. 82, 1875-1876.Wangerin. Berliner Monatsber. 1878.Referenced on Wolfram|Alpha
Cyclidic CoordinatesCite this as:
Weisstein, Eric W. "Cyclidic Coordinates." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CyclidicCoordinates.html