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Cylinder coordinates

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cylindrical coordinates

Numbers and connected with the Cartesian coordinates and by the formulas:

where , , . The coordinate surfaces (see Fig.) are: circular cylinders , half-planes and planes .

Figure: c027600a

The system of cylinder coordinates is orthogonal.

The Lamé coefficients are:

The area element of a surface is:

The volume element is:

The differentiation operations of vector analysis are given by:

Generalized cylinder coordinates are numbers and connected with Cartesian coordinates and by the formulas

where , , , , , , . The coordinate surfaces are: elliptic cylinders , half-planes and planes .


Comments

References

[a1] U.G. Chambers, "A course in vector analysis" , Chapman & Hall (1969)
How to Cite This Entry:
Cylinder coordinates. D.D. Sokolov (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Cylinder_coordinates&oldid=16846
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098