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curl angular velocity ?

From: Kai Habel
Subject: curl angular velocity ?
Date: Mon, 16 Mar 2009 09:43:16 +0100
User-agent: Thunderbird (X11/20081227)

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.



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