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An ellipsoidal section is the curve formed by the intersection of a plane with an ellipsoid. An ellipsoidal section is always an ellipse.

The v coordinates are the asymptotic angle of confocal hyperbolic cylinders symmetrical about the x-axis. The u coordinates are confocal elliptic cylinders centered on the ...

Confocal conics are conic sections sharing a common focus. Any two confocal central conics are orthogonal (Ogilvy 1990, p. 77).

An equation is a mathematical expression stating that two or more quantities are the same as one another, also called an equality, formula, or identity.

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

The word differential has several related meaning in mathematics. In the most common context, it means "related to derivatives." So, for example, the portion of calculus ...

In bispherical coordinates, Laplace's equation becomes (1) Attempt separation of variables by plugging in the trial solution f(u,v,phi)=sqrt(coshv-cosu)U(u)V(v)Psi(psi), (2) ...

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 ...

There are several different definitions of conical coordinates defined by Morse and Feshbach (1953), Byerly (1959), Arfken (1970), and Moon and Spencer (1988). The ...

A system of curvilinear coordinates for which several different notations are commonly used. In this work (u,v,phi) is used, whereas Arfken (1970) uses (xi,eta,phi) and Moon ...