  The ideal Galton board and Lorentz gas billiard models have been studied
numerically and analytically primarily in settings where friction and
rotational velocity are neglected. We eliminate these simplifying assumptions
and study the resulting dynamics of a more general model using no-slip
collisions, in which particles rotate and may exchange linear and angular
momentum at collisions while adhering to certain conservation laws. Using
numerical experiments and phase portrait analysis we show that (in contrast to
specular dispersing billiards) regularity persists when a small force is
introduced while (consistent with specular billiards) under a stronger force
new structure including invariant regions may arise. We also show analytically
that with the introduction of an external force periodicity proliferates, with
new types of periodic orbits not present in the no-force case.
