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# Cylindrical

Cylindrical coordinates are often given as so that is azimuthal in the same sense as spherical polar, and so that is differentiated from . However, many other similar conventions are used. For example, or or are not uncommon. We will use in this review to avoid as much confusion as possible with spherical polar coordinates.

• Vectors: But Note Well: is now a function of ! Similarly: with a function of the angle that defines the direction of . Specifically:

• Unit vectors (relative to Cartesian :   • Direct Length • Directed Area  And again, there are many other possible 's, for example: for an end cap of a cylindrical volume.

• Volume Element for the second of these area elements. • Divergence; The divergence is constructed by the same argument that proves the divergence theorem in a general curvilinear coordinate system given above. • Curl The curl is evaluated in exactly the same way from the expression above, but it ends up being much more complex: • Laplacian The Laplacian follows by applying the divergence rule to the gradient rule and simplifying:     Next: The Dirac -Function Up: Coordinate Systems Previous: Spherical Polar   Contents
Robert G. Brown 2017-07-11