  We present a general treatment of the leading order dynamics of the
collective modes of charged dilatonic $p$-brane solutions of (super)gravity
theories in arbitrary backgrounds. To this end we employ the general strategy
of the blackfold approach which is based on a long-wavelength derivative
expansion around an exact or approximate solution of the (super)gravity
equations of motion. The resulting collective mode equations are formulated as
forced hydrodynamic equations on dynamically embedded hypersurfaces. We derive
them in full generality (including all possible asymptotic fluxes and dilaton
profiles) in a far-zone analysis of the (super)gravity equations and in
representative examples in a near-zone analysis. An independent treatment based
on the study of external couplings in hydrostatic partition functions is also
presented. Special emphasis is given to the forced collective mode equations
that arise in type IIA/B and eleven-dimensional supergravities, where besides
the standard Lorentz force couplings our analysis reveals additional couplings
to the background, including terms that arise from Chern-Simons interactions.
We also present a general overview of the blackfold approach and some of the
key conceptual issues that arise when applied to arbitrary backgrounds.
