Change moment reference frame In a biomechanical model of the human body, moment $\vec M=(M_x, M_y, M_z)$ and force $\vec F=(F_x, F_y, F_z)$ is applied to the pelvis, all expressed in a local (pelvis) reference frame. Additionally, the position $\vec P=(x, y,z)$ and the orientation (pitch, yaw, roll) of the pelvis is given in the lab reference frame.
How do I get moment and force expressed in lab reference frame?
 A: the components of a arbitrary vector that given in body fixed coordinates system, transformed to the initial system with this equation:
$$\vec{F}_L=R\,\vec{F}_P\tag 1$$
where $R$ is the transformation matrix between the  pelvis reference system and Lab system.
$$R=R_z(\psi)\,R_x(\varphi)\,R_y(\vartheta)$$


*

*$\psi$ yaw angle

*$\varphi$ roll angle

*$\vartheta$ pitch angle
$$R_z= \left[ \begin {array}{ccc} \cos \left( \psi \right) &-\sin \left( 
\psi \right) &0\\\sin \left( \psi \right) &\cos
 \left( \psi \right) &0\\ 0&0&1\end {array} \right]
$$
$$R_x=\left[ \begin {array}{ccc} 1&0&0\\0&\cos \left( 
\varphi  \right) &-\sin \left( \varphi  \right) \\0
&\sin \left( \varphi  \right) &\cos \left( \varphi  \right) 
\end {array} \right] 
$$
$$R_y= \left[ \begin {array}{ccc} \cos \left( \vartheta  \right) &0&\sin
 \left( \vartheta  \right) \\ 0&1&0
\\ -\sin \left( \vartheta  \right) &0&\cos \left( 
\vartheta  \right) \end {array} \right] 
$$
and 
$$\vec{M}_L=R\,\vec{M}_P\tag 2$$
the translation vector $\vec{P}$ doesn't affect equations (1) and (2)
