Prolate Spheroidal Coordinates
Alternate name
Definition
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, which is relabeled the z-axis. The third set of coordinates consists of planes passing through this axis. x | = | a sinh ξ sin η cos ϕ y | = | a sinh ξ sin η sin ϕ z | = | a cosh ξ cos η, where ξ element [0, ∞), η element [0, π], and ϕ element [0, 2π). Note that several conventions are in common use; Arfken uses (u, v, φ) instead of (ξ, η, ϕ), and Moon and Spencer use (η, θ, ψ).
