Angular velocity tensor: Difference between revisions

Revision as of 20:01, 18 September 2009

Revision as of 05:15, 3 November 2009

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{{Unreferenced|date=February 2007}}

{{orphan|date=November 2009}}

In [[physics]], the '''angular velocity tensor''' is defined as a matrix T such that:

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==Coordinate-free description==

At any instant, <math>t</math>, the angular velocity tensor is a linear map between the position vectors <math> \mathbf{r}(t) </math>

and their velocity vectors <math> \mathbf{v}(t) </math> of a rigid body rotating around the origin:

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:<math> T\mathbf{r} = \omega \times \mathbf{r}</math>

== Viewing as a vector field ==

For angular velocity tensor maps velocities to positions, it is a [[vector field]]. In particular, this vector field is a [[Killing vector field]] belonging to an element of the [[Lie algebra]] so(3) of the 3-dimensional [[rotation group]], SO(3).

== See also ==

* [[Angular velocity]]

* [[Rigid body dynamics]]

{{DEFAULTSORT:Angular Velocity Tensor}}

[[Category:Physical quantities]]

[[Category:Articles lacking sources (Erik9bot)]]

[[Category:Tensors]]