  We develop general methods to calculate the mobilities of extended bodies in
(or associated with) membranes and films. We demonstrate a striking difference
between in-plane motion of rod-like inclusions and the corresponding case of
bulk (three-dimensional) fluids: for rotations and motion perpendicular to the
rod axis, we find purely local drag, in which the drag coefficient is purely
algebraic in the rod dimensions. These results, as well as the calculational
methods are applicable to such problems as the diffusion of objects in or
associated with Langmuir films and lipid membranes. The methods can also be
simply extended to treat viscoelastic systems.
