Angular velocities and rotation matrices - Robotics Stack Exchange most recent 30 from robotics.stackexchange.com 2020-01-23T12:32:23Z https://robotics.stackexchange.com/feeds/question/8247 https://creativecommons.org/licenses/by-sa/4.0/rdf https://robotics.stackexchange.com/q/8247 2 Angular velocities and rotation matrices charles https://robotics.stackexchange.com/users/10782 2015-10-14T08:43:47Z 2015-10-14T13:59:24Z <p>Let us assume I have an object O with axis $x_{O}$, $y_{O}$, $z_{O}$, with different orientation from the global frame S with $x_{S}$, $y_{S}$, $z_{S}$ (I don't care about the position). Now I know the 3 instantaneous angular velocities of the object O with respect to the same O frame, that is $\omega_O^O = [\omega_{Ox}^O \omega_{Oy}^O \omega_{Oz}^O]$. How can I obtain this angular velocity with respect to the global frame (that is $\omega_O^S$)?</p> <p>Thank you!</p> https://robotics.stackexchange.com/questions/8247/-/8252#8252 4 Answer by Chuck for Angular velocities and rotation matrices Chuck https://robotics.stackexchange.com/users/9720 2015-10-14T13:59:24Z 2015-10-14T13:59:24Z <p>If your object $O$ has a different orientation from your global frame $S$, and you know what that difference in orientation is, you can create a 4x4 transform matrix between the two:</p> <p>$$T = \left[ \begin{array}{cc} R &amp; s \\ 0 &amp; 1 \end{array} \right]$$</p> <p>where $R$ is the 3x3 rotation matrix, $s$ is the 3x1 translation vector, $0$ is a 1x3 row of zeros, and $1$ is just 1. You can transform your (points, angular velocities, etc.) from one frame to another with:</p> <p>$$\left[ \begin{array}{c} x' \\ y' \\ z' \\ 1 \end{array} \right] = \left[ \begin{array}{cc} R &amp; s \\ 0 &amp; 1 \end{array} \right] \left[ \begin{array}{c} x \\ y \\ z \\ 1 \end{array} \right]$$</p> <p>If you don't care about translation you can just set $s = \left[ \begin{array} 00 \\ 0 \\ 0 \\ \end{array} \right]$</p>