  The Einstein equations for a perfect fluid spatially homogeneous spacetime
are studied in a unified manner by retaining the generality of certain
parameters whose discrete values correspond to the various Bianchi types of
spatial homogeneity. A parameter-dependent decomposition of the metric
variables adapted to the symmetry breaking effects of the nonabelian Bianchi
types on the "free dynamics" leads to a reduction of the equations of motion
for those variables to a 2-dimensional time-dependent Hamiltonian system
containing various time-dependent potentials which are explicitly described and
diagrammed. These potentials are extremely useful in deducing the gross
features of the evolution of the metric variables.
