## 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
*height* or *altitude* (if the reference plane is considered horizontal), *longitudinal position*,^{
[1]} or *axial position*.^{
[2]}

Cylindrical coordinates are useful in connection with objects and phenomena that have some rotational

They are sometimes called "cylindrical polar coordinates"^{
[3]} and "polar cylindrical coordinates",^{
[4]} and are sometimes used to specify the position of stars in a galaxy ("galactocentric cylindrical polar coordinates").^{
[5]}

- definition
- coordinate system conversions
- line and volume elements
- cylindrical harmonics
- see also
- references
- further reading
- external links

The three coordinates (

- The radial distance ρ is the
Euclidean distance from the z-axis to the point P. - The azimuth φ is the angle between the reference direction on the chosen plane and the line from the origin to the projection of P on the plane.
- The height z is the signed distance from the chosen plane to the point P.

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* ± (2*n* + 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
*ρ* ≥ 0) and the azimuth φ to lie in a specific

The notation for cylindrical coordinates is not uniform. The
*ρ*, *φ*, *z*), where ρ is the radial coordinate, φ the azimuth, and z the height. However, the radius is also often denoted r or s, the azimuth by θ or t, and the third coordinate by h or (if the cylindrical axis is considered horizontal) x, or any context-specific letter.

In concrete situations, and in many mathematical illustrations, a positive angular coordinate is measured

Other Languages

Afrikaans: Silindriese koördinatestelsel

العربية: نظام إحداثي أسطواني

čeština: Válcová soustava souřadnic

dansk: Cylindrisk koordinatsystem

Deutsch: Polarkoordinaten#Zylinderkoordinaten

Ελληνικά: Κυλινδρικές συντεταγμένες

español: Coordenadas cilíndricas

فارسی: دستگاه مختصات استوانهای

français: Coordonnées cylindriques

한국어: 원통좌표계

हिन्दी: बेलनी निर्देशांक प्रणाली

עברית: קואורדינטות גליליות

latviešu: Cilindriskā koordinātu sistēma

magyar: Hengerkoordináta-rendszer

Nederlands: Cilindercoördinaten

日本語: 円柱座標変換

norsk nynorsk: Sylinderkoordinatsystem

polski: Układ współrzędnych walcowych

português: Coordenadas cilíndricas

русский: Цилиндрическая система координат

slovenščina: Cilindrični koordinatni sistem

српски / srpski: Цилиндрични координатни систем

srpskohrvatski / српскохрватски: Cilindrični koordinatni sistem

svenska: Cylindriska koordinater

Türkçe: Silindirik koordinat sistemi

українська: Циліндрична система координат

中文: 圓柱坐標系