  We study the motion and equilibria of the grains on the surface of the
irregular celestial body (hereafter called irregular bodies). Motions for the
grains on the smooth and unsmooth surfaces are discussed, respectively. The
linearized equations of motion relative to a surface equilibrium point and its
characteristic equations are presented. Considering the stick-slip effect, the
damping forces and the spring forces for the grain are calculated, then the
linearized equations of motion and the characteristic equations relative to the
surface equilibrium points are derived. The number of non-degenerate surface
equilibria is an even number. We compute the motion of a grain released above
three different regions relative to the irregular asteroid 6489 Golevka,
including the flat surface, the concave region, and the convex region.
Following the grain release and initial bounce, three kinds of motions exist,
the orbital motion, the impact motion and the surface motion. We find that the
maximum height of the next hop may be bigger than the maximum height of the
current hopping. We also used Monte Carlo simulations to calculate 100 grains
hopping motions, the results shows that the stable surface equilibria are on
the concave region and flat surface of the asteroid.
