# Cylinder coordinates

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 .