  For systems of the form $\dot q = M^{-1} p$, $\dot p = -Aq+f(q)$, common in
many applications, we analyze splitting integrators based on the
(linear/nonlinear) split systems $\dot q = M^{-1} p$, $\dot p = -Aq$ and $\dot
q = 0$, $\dot p = f(q)$. We show that the well-known Strang splitting is
optimally stable in the sense that, when applied to a relevant model problem,
it has a larger stability region than alternative integrators. This generalizes
a well-known property of the common St\"{o}rmer/Verlet/leapfrog algorithm,
which of course arises from Strang splitting based on the (kinetic/potential)
split systems $\dot q = M^{-1} p$, $\dot p = 0$ and $\dot q = 0$, $\dot p =
-Aq+f(q)$.
