  A general theory of optical forces on moving bodies is here developed in
terms of generalized/4x4 transfer and scattering matrices. Results are
presented for a planar dielectric multilayer of arbitrary refractive index
placed in an otherwise empty space and moving parallel and perpendicular to the
slab-vacuum interface. In both regimes of motion the resulting force comprises
lateral and normal velocity-dependent components which may depend in a subtle
way on the Doppler effect and TE-TM polarization mixing. For lateral
displacements in particular, polarization mixing, which is here interpreted as
an effective magneto-electric effect due to the reduced symmetry induced by the
motion of the slab, gives rise to a velocity dependent force contribution that
is sensitive to the phase difference between the two polarization amplitudes.
This term gives rise to a rather peculiar optical response on the moving body
and specific caseses are illustrated for incident radiation of arbitrarily
directed linear polarization. The additional force due to polarization mixing
may cancel to first order in V/c with the first order Doppler contribution
yielding an overall vanishing of the velocity-dependent component of the force
on the body. The above findings bare some relevance to modern developments of
nano-optomechanics as well as to the problem of a frictional component to the
Casimir force.
