Cylindrical coordinate system

A three-dimensional coordinate system that locates a point by its distance from an axis, its angle around that axis, and its position along it.

Cylindrical-to-Cartesian coordinate conversion: The conversion between cylindrical coordinates and Cartesian coordinates using planar trigonometry. The radial distance and angle determine the point’s two Cartesian coordinates.
Cartesian coordinate system: A coordinate system that locates points using signed distances along mutually perpendicular axes. It provides the rectangular coordinates related to cylindrical measurements.
Cylindrical symmetry: Invariance under rotations about an axis and translations along that axis. Such symmetry often makes cylindrical coordinates simplify equations.
Spherical coordinate system: A three-dimensional coordinate system that locates points by distance from an origin and two angles. It suits symmetry about a point rather than a single axis.
Cylindrical unit vectors: The position-dependent radial, azimuthal, and axial basis vectors used in cylindrical geometry. These directions express vectors in a basis aligned with the system’s geometry.
Polar coordinate system: A two-dimensional coordinate system that locates points by distance from an origin and angle from a reference direction. Cylindrical coordinates extend polar coordinates with an axial position.
Cylindrical shell method: An integration method that computes volumes using thin cylindrical shells. Shells are naturally described by radius, angle, and axial position.
Elliptic cylindrical coordinates: A three-dimensional orthogonal coordinate system whose constant-coordinate surfaces include confocal elliptic cylinders. Its elliptical cross-sections replace the circular geometry of standard cylindrical coordinates.
Cylindrical coordinate Jacobian: The determinant factor that adjusts volume integrals when converting to cylindrical coordinates. Its radial factor accounts for the changing size of angular intervals.
Azimuth: The angle around a reference axis or direction, measured in a plane perpendicular to that axis. It specifies the point’s rotation around the cylindrical axis.

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