Let $Z,X,Y$ be instantaneous observers, such that $X=\b(Z+uE)$, $Y=\g(X+vF)$, where $E\perp Z$ and $F\perp X$ are unit vectors. Determine the energy $e$ and the momentum $P$ of $Y$ with respect to $Z$ in terms of $Z$, $E$ and $F$.
The energy is given by
$$
e=-\la Y,Z\ra=-\la\g(X+vF),Z\ra=\g\b-\g v\la F,Z\ra
$$
and since $Z=(X-\b uE)/\b$ and $F\perp X$, we get: $e=\g\b+\g uv\la E,F\ra$.
\begin{eqnarray*}
P&=&Y+\la Y,Z\ra Z\\
&=&\g(X+vF)-eZ\\
&=&\g(\b(Z+uE)+vF)-(\g\b+\g\la uE,vF\ra)Z\\
&=&\g(-uv\la E,F\ra Z+\b uE+vF)
\end{eqnarray*}
This is sort of hybrid description, for $E$ is in the rest space of $Z$ and $F$ is in the rest space of $X$!