Angular velocity tensor: Difference between revisions

Revision as of 12:33, 14 June 2007

Revision as of 12:35, 14 June 2007

Line 2:

:<math>

\boldsymbol\omega(t) \times A(t)\mathbf{r}_0 = T(t)A(t)\mathbf{r}_0 =</math>

where A is an [[orientation matrix]]. It allows us to express the [[cross product]]

:<math>\boldsymbol\omega(t) \times A(t)\mathbf{r}_0 </math>

as a matrix multiplication. It is, by definition, a [[skew-symmetric matrix]] with zeros on the main diagonal and plus and minus the components of the angular velocity as the other elements.:

:</math>

T(t) =

\begin{pmatrix}

0 & -\omega_z(t) & \omega_y(t) \\

\omega_z(t) & 0 & -\omega_x(t) \\

-\omega_y(t) & \omega_x(t) & 0 \\

\end{pmatrix} A(t)\mathbf{r}_0.</math>

</math>

where A is an [[orientation matrix]]. It allows us to express the [[cross product]]

:<math>\boldsymbol\omega(t) \times A(t)\mathbf{r}_0 </math>

as a matrix multiplication. It is, by definition, a [[skew-symmetric matrix]] with zeros on the main diagonal and plus and minus the components of the angular velocity as the other elements.

== See also ==