TDHF equations of motion for algebraic hamiltonians in a coherent state representation

Time-dependent Hartee-Fock (TDHF) equations are derived for nuclear systems with internal dynamical group U(r). The coordinates which appear in the TDHF equations are the coordinates which parameterize the U(r) coherent states. The TDHF orbits for the hamiltonian $\text{H}$ are identical with equations of motion for a classical system described by the hamiltonian function 〈$\text{H}$〉 obtained directly from the operator $\text{H}$. This quantum-classical correspondence facilitates interpretation of TDHF orbits. The phenomena of coexistence and critical elongation are discusses, as is the relation between the critical points of the function 〈$\text{H}$〉 and the spectral properties fo the operator $\text{H}$.