# Cylinder coordinates

From Encyclopedia of Mathematics

*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