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Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition
book

Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition

by Andrei D. Polyanin, Vladimir E. Nazaikinskii
December 2015
Intermediate to advanced content levelIntermediate to advanced
1643 pages
59h 33m
English
Chapman and Hall/CRC
Content preview from Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition
Chapter 2 9
Curvilinear Coordinates, Vectors,
Operators, and Differential
Relations
29.1 Arbitrary Curvilinear Coordinate Systems
29.1.1 G eneral Nonorthogonal Curvilinear Coordinates
Metric tensor. Arc length and volume elements in curvilinear coordinates.
The curvilinear coordinates x
1
, x
2
, x
3
are defined as functions of the rectangular Cartesian
coordinates x, y, z:
x
1
= x
1
(x, y, z), x
2
= x
2
(x, y, z), x
3
= x
3
(x, y, z).
Using these formulas, one can express x, y, z in terms of the curvilinear coordinates
x
1
, x
2
, x
3
as follows:
x = x(x
1
, x
2
, x
3
), y = y(x
1
, x
2
, x
3
), z = z(x
1
, x
2
, x
3
).
The metric tensor components g
ij
are determined by the formulas
g
ij
(x
1
, x
2
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Publisher Resources

ISBN: 9781466581494