  The dynamics of a set of rods bouncing on a vertically vibrated plate is
investigated using experiments, simulations, and theoretical analysis. The
experiments and simulations are performed within an annulus to impose periodic
boundary conditions. Rods tilted with respect to the vertical are observed to
spontaneously develop a horizontal velocity depending on the acceleration of
the plate. For high plate acceleration, the rods are observed to always move in
the direction of tilt. However, the rods are also observed to move opposite to
direction of tilt for a small range of plate acceleration and rod tilt. A phase
diagram of the observed motion is presented as a function of plate acceleration
and the tilt of the rods which is varied by changing the number of rods inside
the annulus. Next we introduce a novel molecular dynamics method to simulate
the dynamics of the rods using the dimensions and dissipation parameters from
the experiments. We reproduce the observed horizontal rod speeds as a function
of rod tilt and plate acceleration in the simulations. By decreasing the
friction between the rods and the base plate to zero in the simulation, we
identify the friction during the collision as the crucial ingredient for
occurrence of the horizontal motion. Guided by the data from the experiments
and the simulations, we construct a mechanical model for the dynamics of the
rods in the limit of thin rods. The starting point of the analysis is the
collision of a single rod with an oscillating plate. Three friction regimes are
identified: slide, slip-stick, and slip reversal. A formula is derived for the
observed horizontal velocity as a function of tilt angle. Good agreement for
the horizontal velocity as a function of rod tilt and plate acceleration is
found between experiments, simulations and theory.
