  We consider two linearly coupled masses, where one mass can have inelastic
impacts with a fixed, rigid stop. This leads to the study of a two degree of
freedom, piecewise linear, frictionless, unforced, constrained mechanical
system. The system is governed by three types of dynamics: coupled harmonic
oscillation, simple harmonic motion and discrete rebounds. Energy is dissipated
discontinuously in discrete amounts, through impacts with the stop. We prove
the existence of a nonzero measure set of orbits that lead to infinite impacts
with the stop in a finite time. We show how to modify the mathematical model so
that forward existence and uniqueness of solutions for all time is guaranteed.
Existence of hybrid periodic orbits is shown. A geometrical interpretation of
the dynamics based on action coordinates is used to visualize numerical
simulation results for the asymptotic dynamics.
