Cylindrical Coordinate Cylindrical coordinates are a generalization of two-dimensionalpolar coordinatesto three dimensions by superposing a height ( ) axis. Unfortunately, there are a number of different notations used for the other two coordinates. Either or is used to refer to the radial coordinate and either or to the azimuthal coordinates. rf!en ("#$%), for instance, uses , while &eyer ("#$') uses . n this wor!, thenotationis used. he following table summarizes notational con*entions used by a number of authors. (radial, azimuthal, *ertical) reference this wor!, &eyer ("#$', p. +"+) (Rr, Ttheta, Zz) SetCoordinates Cylindricalin the Mathematicapac!age VectorAnalysis` rf!en ("#$%, p. # %) oon and /pencer ("#$$, p. "+) 0orn and 0orn ("#1$, p. 12) orse and 3eshbach ("#%4) n terms of the Cartesian coordinates , (") (+) (4) where , , , and thein*erse tangentmust be suitably defined to ta!e the correct 5uadrant of into account. n terms of , , and
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Cylindrical coordinates are a generalization of two-dimensional polar coordinates to three dimensions by superposinga height ( ) axis. Unfortunately, there are a number of different notations used for the other two coordinates. Either
or is used to refer to the radial coordinate and either or to the azimuthal coordinates. rf!en ("#$%), for
instance, uses , while &eyer ("#$') uses . n this wor!, thenotation is used.
he following table summarizes notational con*entions used by a number of authors.
(radial, azimuthal,*ertical)
reference
this wor!, &eyer ("#$', p. +"+)
(Rr, Ttheta, Zz) SetCoordinatesCylindrical in
the Mathematica pac!age VectorAnalysis`
rf!en ("#$%, p. #%)
oon and /pencer ("#$$, p. "+)
0orn and 0orn ("#1$, p. 12)
orse and 3eshbach ("#%4)
n terms of the Cartesian coordinates ,
(")
(+)
(4)
where , , , and the in*erse tangent must be suitably defined to ta!e the correct