Cylindrical Coordinates

cylindrical coordinates

[sə′lin·drə·kəl ‚kō′ȯrd·ən·əts]

(mathematics)

A system of curvilinear coordinates in which the position of a point in space is determined by its perpendicular distance from a given line, its distance from a selected reference plane perpendicular to this line, and its angular distance from a selected reference line when projected onto this plane.

Cylindrical Coordinates

 

The cylindrical coordinates of a point M are the three numbers r, θ, and z characterizing the position of M in space (see Figure 1). The coordinates are called cylindrical because the coordinate surface r = const is a cylinder

Figure 1

whose elements are parallel to the z-axis. The relation between the cylindrical coordinates and the rectangular coordinates x, y, and z of M is given by the equations x = r cos θ, y = r sin θ, and z = z.