  We derive conditions under which a general nonlinear mechanical system can be
exactly reduced to a lower-dimensional model that involves only the most
flexible degrees of freedom. This Slow-Fast Decomposition (SFD) enslaves
exponentially fast the stiff degrees of freedom to the flexible ones as all
oscillations converge to the reduced model defined on a slow manifold. We
obtain an expression for the domain boundary beyond which the reduced model
ceases to be relevant due to a generic loss of stability of the slow manifold.
We also find that near equilibria, the SFD gives a mathematical justification
for two modal-reduction methods used in structural dynamics: static
condensation and modal derivatives. These formal reduction procedures, however,
are also found to return incorrect results when the SFD conditions do not hold.
We illustrate all these results on mechanical examples.
