  We introduce a model of uncoupled pendula, which mimics the dynamical
behavior of the Hamiltonian Mean Field (HMF) model. This model has become a
paradigm for long-range interactions, like Coulomb or dipolar forces. As in the
HMF model, this simplified integrable model is found to obey the Vlasov
equation and to exhibit Quasi Stationary States (QSS), which arise after a
"collisionless" relaxation process. Both the magnetization and the single
particle distribution function in these QSS can be predicted using
Lynden-Bell's theory. The existence of an extra conserved quantity for this
model, the energy distribution function, allows us to understand the origin of
some discrepancies of the theory with numerical experiments. It also suggests
us an improvement of Lynden-Bell's theory, which we fully implement for the
zero field case.
