A set of curvilinear coordinates defined by x | = | (a sinh v)/(cosh v - cos u) y | = | (a sin u)/(cosh v - cos u) z | = | z, where u element [0, 2π), v element (-∞, ∞), and z element (-∞, ∞). There are several notational conventions, and whereas (u, v, z) is used in this work, Arfken prefers (η, ξ, z). The following identities show that curves of constant u and v are circles in x y-space. x^2 + (y - a cot u)^2 = a^2 csc^2 u (x - a coth v)^2 + y^2 = a^2 csch^2 v.

bipolar coordinates | polar coordinates