  Current theories of dynamical friction on galactic bars are based either on
linear perturbation theory, which is valid only in the fast limit where the bar
changes its pattern speed rapidly, or on adiabatic theory, which is applicable
only in the slow limit where the bar's pattern speed is near-constant. In this
paper, we study dynamical friction on galactic bars spinning down at an
arbitrary speed, seamlessly connecting the fast and slow limits. We treat the
bar-halo interaction as a restricted $N$-body problem and solve the
collisionless Boltzmann equation using the fast-angle-averaged Hamiltonian. The
phase-space distribution and density wakes predicted by our averaged model are
in excellent agreement with full 3D simulations. In the slow regime where
resonant trapping occurs, we show that, in addition to the frictional torque,
angular momentum is transferred directly due to the migration of the trapped
phase-space: trapped orbits comoving with the resonance typically gain angular
momentum, while untrapped orbits leaping over the trapped island lose angular
momentum. Due to the negative gradient in the distribution function, gainers
typically outnumber the losers, resulting in a net negative torque on the
perturber. Part of this torque due to the untrapped orbits was already
identified by Tremaine & Weinberg who named the phenomenon dynamical feedback.
Here, we derive the complete formula for dynamical feedback, accounting for
both trapped and untrapped orbits. Using our revised formula, we show that
dynamical feedback can account for up to $30\%$ of the total torque on the
Milky Way's bar.
