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A set of quadratic surfaces which share foci. Ellipsoids and one- and two-sheeted hyperboloids can be confocal. These three types of surfaces can be combined to form an ...

A transformation T (a.k.a., map, function) over a domain D takes the elements X in D to elements Y in T(D), where the range (a.k.a., image) of T is defined as ...

A system of curvilinear coordinates in which two sets of coordinate surfaces are obtained by revolving the curves of the elliptic cylindrical coordinates about the x-axis, ...

A formula which transforms a given coordinate system by rotating it through a counterclockwise angle Phi about an axis n^^. Referring to the above figure (Goldstein 1980), ...

The coordinate system obtained by inversion of Cartesian coordinates, with u,v,w in (-infty,infty). The transformation equations are x = u/(u^2+v^2+w^2) (1) y = ...

A coordinate system which is similar to bispherical coordinates but having fourth-degree surfaces instead of second-degree surfaces for constant mu. The coordinates are given ...

A coordinate system obtained by inversion of the bicyclide coordinates. They are given by the transformation equations x = Lambda/(aUpsilon)snmudnnucospsi (1) y = ...

A coordinate system defined by the transformation equations x = a/Lambdacnmucnnucospsi (1) y = a/Lambdacnmucnnusinpsi (2) z = a/Lambdasnmudnmusnnudnnu, (3) where ...

A coordinate system similar to toroidal coordinates but with fourth-degree instead of second-degree surfaces for constant mu so that the toroids of circular cross section are ...

A system of coordinates obtained by inversion of the oblate spheroids and one-sheeted hyperboloids in oblate spheroidal coordinates. The inverse oblate spheroidal coordinates ...