This is related to this question Confusion in coordinate transformation of acceleration vector. My confusion arises for the position vector, does velocity vector follow the same logic as acceleration?
I mean:
$$ p^e_{cb} = R^e_d * p^e_{cb} $$
and according to the answer of related question, since $v^d_{cb} \neq \dot{p}^d_{cb}$ I expect the same develop for velocity vector. $$\dot{p}_{cb}^{e}=\dot{R}_{d}^{e}p_{cb}^{d}+R_{d}^{e} \dot{p}_{cb}^{d}$$
My confusion came because I found an article and they have a position vector $S = [x \hspace{2mm} y]^T$, then they have $\dot{S} = R*\dot{S}_m$ and the same develop for $\ddot{S} = \dot{R}*\dot{S}_m + R \ddot{S}_m$, they don't use R matrix with a position vector but with a force vector as $F = R*F_m$
In my case I need to use also a transformation for position vector as well as acceleration vector but I'm not sure if $S = R*S_m$ is valid
