  We show by symplectic realizations of the one dimensional Static group $G$
that the maximal $G$-elementary system is a a massive particle under an
invariant force $f$ participating in the linear momentum and an invariant
impetus $I$ participating in the change of position. Moreover the system is
characterized by four physical quantities : a mass $m$, a boost
$u=\frac{I}{m}$, an acceleration $a=\frac{f}{m}$ and an internal energy $U$.
The hamiltonian of the system is a sum of the potential energy $V=-fq$ and a
contribution $pu$ of the impetus.
