  When a Hamiltonian system is subject to constraints which depend explicitly
on time, difficulties can arise in attempting to reduce the system to its
physical phase space. Specifically, it is non-trivial to restrict the system in
such a way that one can find a Hamiltonian time-evolution equation involving
the Dirac bracket. Using a geometrical formulation, we derive an explicit
condition which is both necessary and sufficient for this to be possible, and
we give a formula defining the resulting Hamiltonian function. Some previous
results are recovered as special cases.
