  We study classical energy-momentum ($E$-$m$) diagrams for rotational motion
of dipolar asymmetric top molecules in strong external fields. Static electric
fields, nonresonant linearly polarized laser fields, and collinear combinations
of the two are investigated. We treat specifically the molecules iodobenzene (a
nearly prolate asymmetric top), pyridazine (nearly oblate asymmetric top), and
iodopentafluorobenzene (intermediate case). The location of relative equilibria
in the $E$-$m$ plane and associated bifurcations are determined by
straightforward calculation, with analytical results given where possible. In
cases where analytical solutions cannot be obtained, we resort to numerical
solutions, while keeping a geometrical picture of the nature of the solutions
to the fore. The classification we obtain of the topology of classically
allowed rotor configuration space regions in the $E$-$m$ diagram is of
potential use in characterization of energy eigenstates of the corresponding
quantum mechanical problem.
