Numbers and connected with the Cartesian coordinates and by the formulas:
where , , . The coordinate surfaces (see Fig.) are: circular cylinders , half-planes and planes .
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 .
|[a1]||U.G. Chambers, "A course in vector analysis" , Chapman & Hall (1969)|
Cylinder coordinates. D.D. Sokolov (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Cylinder_coordinates&oldid=16846