Numbers , and related to the rectangular Cartesian coordinates , and by the formulas
where , , . The coordinate surfaces are two systems of paraboloids of revolution with oppositely-directed axes ( and ) and half-planes (). The system of paraboloidal coordinates is orthogonal.
The Lamé coefficients (or scale factors) are
The element of surface area is
The volume element is
The fundamental operations of vector analysis are
These coordinates are also called rotation parabolic coordinates.
|[a1]||R. Sauer (ed.) I. Szabó (ed.) , Mathematische Hilfsmittel des Ingenieurs , 1 , Springer (1967) pp. 96|
Paraboloidal coordinates. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Paraboloidal_coordinates&oldid=11852