1.7: Coordinate Systems
By the end of this section, you will be able to
- Identify the key differences between Cartesian, cylindrical, and spherical systems.
The coordinate systems most commonly used in scientific and engineering analysis are the Cartesian [1], cylindrical [2], and spherical [3] systems. These systems are illustrated in Figures \(\PageIndex{1}\), \(\PageIndex{2}\), and \(\PageIndex{3}\), respectively.
Note that the use of variables is not universal; in particular, it is common to encounter the use of \(r\) in lieu of \(\rho\) for the radial coordinate in the cylindrical system, and the use of \(R\) in lieu of \(r\) for the radial coordinate in the spherical system. The angle \(\phi \) is typically called the azimuthal coordinate in both the cylindrical and spherical coordinates, while the angle \(\theta \) is typically called the polar coordinate in spherical coordinates. In contrast to Cartesian coordinates, in which the coordinate unit vectors \(\hat{x}\), \(\hat{y}\), \(\hat{z}\) always point in the same direction, the unit vectors in cylindrical and spherical coordinates will change direction based on the point in space that is being referenced, as indicated in the figures.
References
- Wikipedia contributors. Cartesian coordinate system [Internet]. Wikipedia, The Free Encyclopedia.
- Wikipedia contributors. Cylindrical coordinate system [Internet]. Wikipedia, The Free Encyclopedia.
- Wikipedia contributors. Spherical coordinate syste m [Internet]. Wikipedia, The Free Encyclopedia.
- Wikimedia Commons contributors. File: M0006 fCartesianBasis.svg [Internet]. Wikimedia Commons. (CC BY-SA 4.0; K. Kikkeri)
- Wikimedia Commons contributors. File: M0096 fCylindricalCoordinates.svg [Internet]. Wikimedia Commons. (CC BY-SA 4.0; K. Kikkeri)
- Wikimedia Commons contributors. File: Spherical Coordinate System.svg [Internet]. Wikimedia Commons. (CC BY-SA 4.0; K. Kikkeri)