Cylindrical coordinate system
A cylindrical coordinate system is a three-dimensional
The origin of the system is the point where all three coordinates can be given as zero. This is the intersection between the reference plane and the axis.
The axis is variously called the cylindrical or longitudinal axis, to differentiate it from the polar axis, which is the
The distance from the axis may be called the radial distance or radius, while the angular coordinate is sometimes referred to as the angular position or as the azimuth.The radius and the azimuth are together called the polar coordinates, as they correspond to a two-dimensional
Cylindrical coordinates are useful in connection with objects and phenomena that have some rotational
They are sometimes called "cylindrical polar coordinates" and "polar cylindrical coordinates", and are sometimes used to specify the position of stars in a galaxy ("galactocentric cylindrical polar coordinates").
As in polar coordinates, the same point with cylindrical coordinates (ρ, φ, z) has infinitely many equivalent coordinates, namely (ρ, φ ± n×360°, z) and (−ρ, φ ± (2n + 1)×180°, z), where n is any integer. Moreover, if the radius ρ is zero, the azimuth is arbitrary.
In situations where someone wants a unique set of coordinates for each point, one may restrict the radius to be
The notation for cylindrical coordinates is not uniform. The
In concrete situations, and in many mathematical illustrations, a positive angular coordinate is measured