  We consider a system of two linear and linearly coupled oscillators with
ideal impact constraints. Primary resonant energy exchange is investigated by
analysis of the slow-flow using the action-angle (AA) formalism. Exact
inversion of the action-energy dependence for the linear oscillator with impact
constraints is not possible. This difficulty, typical for many models of
nonlinear oscillators, is circumvented by matching the asymptotic expansions
for the linear and impact limits. The obtained energy-action relation enables
the complete analysis of the slow-flow and the accurate description of the
critical delocalization transition. The transition from the localization regime
to the energy-exchange regime is captured by prediction of the critical
coupling value. Accurate prediction of the delocalization transition requires
detailed account of the coupling energy with appropriate re-definition and
optimization of the limiting phase trajectory on the resonant manifold.
