circular-cylinder coordinates | circular cylindrical coordinates | cylindrical coordinate system

Cylindrical coordinates are a generalization of two-dimensional polar coordinates to three dimensions by superposing a height (z) axis. Unfortunately, there are a number of different notations used for the other two coordinates. Either r or ρ is used to refer to the radial coordinate and either ϕ or θ to the azimuthal coordinates. Arfken, for instance, uses (ρ, ϕ, z), while Beyer uses (r, θ, z). In this work, the notation (r, θ, z) is used. The following table summarizes notational conventions used by a number of authors.

Cartesian coordinates | elliptic cylindrical coordinates | Helmholtz differential equation--circular cylindrical coordinates | polar coordinates | spherical coordinates