Cylindrical coordinate system
The cylindrical coordinate system is a three-dimensional system which essentially extends circular polar coordinates by adding a third coordinate (usually denoted ) which measures the height of a point above the plane.
A point P is given as . In terms of the Cartesian coordinate system:
- is the distance from O to P', the orthogonal projection of the point P onto the XY plane. This is the same as the distance of P to the z-axis.
- is the angle between the positive x-axis and the line OP', measured anti-clockwise.
- is the same as .
Cylindrical coordinates are useful in analyzing surfaces that are symmetrical about an axis, with the z-axis chosen as the axis of symmetry. For example, the infinitely long circular cylinder that has the Cartesian equation x2 + y2 = c2 has the very simple equation r = c in cylindrical coordinates. Hence the name "cylindrical" coordinates.
Conversion from Cartesian to cylindrical coordinates
Conversion from cylindrical to Cartesian coordinates
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Conversion from cylindrical to spherical coordinates
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Conversion from spherical to cylindrical coordinates