一种四阶的通用曲线坐标系统,基于环状线,其中拉普拉斯方程是可分离的(简单可分离或 -可分离)。Bôcher (1894) 处理了此类所有可能的系统 (Moon and Spencer 1988, p. 49)。
Cyclidic 坐标
另请参阅
双环线坐标, 帽状环状线坐标, 盘状环状线坐标, 正交坐标系使用 Wolfram|Alpha 探索
参考文献
Bôcher, M. Über die Reihenentwicklungen der Potentialtheorie. 德国莱比锡: 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. 纽约: 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. 纽约: Springer-Verlag, 1988.Wangerin. Preisschriften der Jablanowski'schen Gesellschaft, No. 18, 1875-1876.Wangerin. Crelle's J. 82, 1875-1876.Wangerin. Berliner Monatsber. 1878.在 Wolfram|Alpha 中被引用
Cyclidic 坐标请引用为
Weisstein, Eric W. "Cyclidic 坐标。" 来自 MathWorld—— Wolfram 网络资源。 https://mathworld.net.cn/CyclidicCoordinates.html