On Sat, Apr 25, 2009 at 4:23 PM, Anders Logg <logg@xxxxxxxxx> wrote:
On Sat, Apr 25, 2009 at 03:10:07PM +0100, Garth N. Wells wrote:
On Apr 25 2009, Anders Logg wrote:
On Sat, Apr 25, 2009 at 11:40:35AM +0200, Martin Sandve Alnæs wrote:
I've verified the curl vs wikipedia and defined rot as the z-component
of the curl of the 2D vector operand embedded in 3D. Is that right?
rot is just a synonym for curl. For simplicity, I would remove rot.
I'm used to the following notation (in pseudo-math):
rot: R^2 --> R
So this can be defined as
nabla x (a(x,y), b(x,y), 0)
=
| i j k |
| ,x ,y ,z |
| a b 0 |
=
(b,x - a,y) k
rot( (a,b) ) = (b,x - a,y)
(or curl)
curl: R --> R^2
How is this defined?
curl( a(x,y) )
=
nabla x (0, 0, a)
=
| i j k |
| ,x ,y ,z |
| 0 0 a |
=
a,y i - a,x j
?
Is this only defined in 2D so we can say curl(constant) = (0, 0)?
(That would simplify some things, but it's not the case for grad.)
curl: R^3 --> R^3
I don't have any opinion on the names rot and curl.
Seems like either definition is just as good to me.
