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 $\omega_O^S$)?
Thank you!