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Euler-Cromer formulation
We rewrite
mu'' + f(u') + s(u) = F(t),\quad u(0)=I,\ u'(0)=V,\ t\in (0,T]
as a first-order ODE system
\begin{align*}
u' &= v
\\
v' &= m^{-1}\left(F(t) - f(v) - s(u)\right)
\end{align*}