  We introduce the concept of a "transitory" dynamical system---one whose
time-dependence is confined to a compact interval---and show how to quantify
transport between two-dimensional Lagrangian coherent structures for the
Hamiltonian case. This requires knowing only the "action" of relevant
heteroclinic orbits at the intersection of invariant manifolds of "forward" and
"backward" hyperbolic orbits. These manifolds can be easily computed by
leveraging the autonomous nature of the vector fields on either side of the
time-dependent transition. As illustrative examples we consider a
two-dimensional fluid flow in a rotating double-gyre configuration and a simple
one-and-a-half degree of freedom model of a resonant particle accelerator. We
compare our results to those obtained using finite-time Lyapunov exponents and
to adiabatic theory, discussing the benefits and limitations of each method.
