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).
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.
| 
Contact the MathWorld Team
