7.1 Polar coordinates
Polar coordinates in two dimensions are
defined by
as indicated schematically in Fig.
7.1
.
Using the chain rule we find
We can write
where the unit vectors
are an orthonormal set. We say that circular
coordinates are
orthogonal.
We can now use this to evaluate
,
A final useful relation is the
integration over these coordinates.
As indicated schematically in Fig.
7.2
, the surface related to a
change
,
is
. This leads us to the conclusion that an integral over
can be rewritten as
|
(7.9) |