  The discovery of over 50 planets around evolved stars and more than 35 debris
discs orbiting white dwarfs highlight the increasing need to understand small
body evolution around both early and asymptotic giant branch (GB) stars.
Pebbles and asteroids are susceptible to strong accelerations from the intense
luminosity and winds of GB stars. Here, we establish equations that can model
time-varying GB stellar radiation, wind drag and mass loss. We derive the
complete three-dimensional equations of motion in orbital elements due to (1)
the Epstein and Stokes regimes of stellar wind drag, (2) Poynting-Robertson
drag, and (3) the Yarkovsky drift with seasonal and diurnal components. We
prove through averaging that the potential secular eccentricity and inclination
excitation due to Yarkovsky drift can exceed that from Poynting-Robertson drag
and radiation pressure by at least three orders of magnitude, possibly flinging
asteroids which survive YORP spin-up into a widely dispersed cloud around the
resulting white dwarf. The GB Yarkovsky effect alone may change an asteroid's
orbital eccentricity by ten per cent in just one Myr. Damping perturbations
from stellar wind drag can be just as extreme, but are strongly dependent on
the highly uncertain local gas density and mean free path length. We conclude
that GB radiative and wind effects must be considered when modelling the
post-main-sequence evolution of bodies smaller than about 1000 km.
