Skew-symmetric matrix property

[ryan88]

This page (https://shiyuzhao.wordpress.com/2011/06/08/rotation-matrix-angle-axis-angular-velocity/), gives the following relation:

$\left[R\vec{\omega}\right]_{\times}=R\left[\vec{\omega}\right]_{\times}R^{T}$

Where:

* $R$ is a DCM (Direction Cosine Matrix)
* $\vec{v}$ is the angular velocity vector
* $[\enspace]_{\times}$ represents a skew-symmetric matrix

I'm not sure where this came from. Is it some inherent property of a skew-symmetric matrix?

 

[MarcusAgrippa]

Looks like the transformation law for the skew symmetric matrix. To understand it, you will need to understand the notation first. It may help you to know that the statement reads: the skew symmetric matrix of the transformed angular velocity vector is equal to the transform of the skew symmetric matrix of the original angular velocity vector.

A large number of "problems" are traceable to knowing the definitions and to understanding the notation.

See if this comment helps you unravel your difficulty.