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## Re: curl angular velocity ?

**From**: |
Kai Habel |

**Subject**: |
Re: curl angular velocity ? |

**Date**: |
Tue, 17 Mar 2009 21:11:41 +0100 |

**User-agent**: |
Thunderbird 2.0.0.19 (X11/20081227) |

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