  We study a two-dimensional gas of inelastic smooth hard dimers. Since the
collisions between dimers are dissipative, being characterized by a coefficient
of restitution $\alpha<1$, and no external driving force is present, the energy
of the system decreases in time and no stationary state is achieved. However,
the resulting non equilibrium state of the system displays several interesting
properties in close analogy with systems of inelastic hard spheres, whose
relaxational dynamics has been thoroughly explored. We generalise to inelastic
systems a recently method introduced [G.Ciccotti and G.Kalibaeva, J. Stat.
Phys. {\bf 115}, 701 (2004)] to study the dynamics of rigid elastic bodies made
up of different spheres hold together by rigid bonds. Each dimer consists of
two hard disks of diameter $d$, whose centers are separated by a fixed distance
$a$. By describing the rigid bonds by means of holonomic constraints and
deriving the appropriate collision rules between dimers, we reduce the dynamics
to a set of equations which can be solved by means of event driven simulation.
After deriving the algorithm we study the decay of the total kinetic energy,
and of the ratio between the rotational and the translational kinetic energy of
inelastic dimers. We show numerically that the celebrated Haff's homogeneous
cooling law $t^{-2}$, describing how the kinetic energy of an inelastic hard
sphere system with constant coefficient of restitution decreases in time, holds
even in the case of these non spherical particles. We fully characterize this
homogeneous decay process in terms of appropriate decay constants and confirm
numerically the scaling behavior of the velocity distributions.
