  Shapere and Wilczek recently found some singular Lagrangian systems which
spontaneously breaks time translation symmetry. The common feature of their
models is that the energy functions are multivalued in terms of the canonical
phase space variables and the symmetry breaking ground states are all located
at the brunching point singularities. By enlarging the phase space and making
use of Dirac's theory on constrained Hamiltonian systems, we present the
Hamiltonian description of some of the models discussed by Shapere and Wilczek
and found that both the multivaluedness and the brunching point singularities
can be avoided, while the spontaneous breaking oftime translation becomes more
transparent. It is also shown that the breaking of time translation is always
accompanied by the breaking of time reversal.
