Re: curl angular velocity ?

[Kai Habel]

Kai Habel schrieb:
> Hello all,
>
> I have almost completed an implementation of divergence and curl for
> octave except for one return parameter. According to matlab
> documentation [1] it is  called "curl angular velocity (cav)". I found
> the documentation not very descriptive. This is what I have found so far:
>
> In a 2d vector field v= [v_x(x,y); v_y(x,y)] "cav" it is calculated by
> means of cav = 1/2*curl(v). This is the more common angular velocity
> vector or more exact its z-component (x- and y- are zero).
>
> Now my questions:
>
> What is curl angular velocity (cav) in 3d?
> It should be related to the angular velocity vector 1/2*curl(v), but
> since cav is a scalar (it can be positive and negative) there must be
> something else.
>
> My internet and text book research was not very successful - it seems
> the term "curl angular velocity" is only used by matlab. Maybe it is
> more common with a different name in some specific areas of engineering,
> like fluid dynamics or atmospheric research.
>
> So, if you could point me to web site or paper (beside the matlab source
> of course!), where curl angular velocity (for 3d) is explained, that
> would very helpful.
>
> Kai
>
> [1]
> http://www.mathworks.de/access/helpdesk/help/techdoc/index.html?/access/helpdesk/help/techdoc/ref/f16-6011.html
>   
I think I have found the solution. I don't know why I have not seen it
earlier.

The first equation @Mathworld [1] gives the answer to my question. When
F and n are replaced by v and v/norm(v) respectively cav can be
calculated by:

cav =  1/2 * dot (curl(v), v/norm(v))

at each point. I will do some more tests and prepare a changeset for
curl and divergence soon.
Sorry for my monologue,

Kai

[1] http://mathworld.wolfram.com/Curl.html