  We show how the classical action, an adiabatic invariant, can be preserved
under non-adiabatic conditions. Specifically, for a time-dependent Hamiltonian
$H = p^2/2m + U(q,t)$ in one degree of freedom, and for an arbitrary choice of
action $I_0$, we construct a "fast-forward" potential energy function $V_{\rm
FF}(q,t)$ that, when added to $H$, guides all trajectories with initial action
$I_0$ to end with the same value of action. We use this result to construct a
local dynamical invariant $J(q,p,t)$ whose value remains constant along these
trajectories. We illustrate our results with numerical simulations. Finally, we
sketch how our classical results may be used to design approximate quantum
shortcuts to adiabaticity.
