  The origin of galactic spiral arms is one of fundamental problems in
astrophysics. Based on the local analysis Toomre (1981) proposed the swing
amplification mechanism in which the self-gravity forms spiral arms as leading
waves of stars rotate to trailing ones due to galactic shear. The structure of
spiral arms is characterized by their number and pitch angle. We perform global
$N$-body simulations of spiral galaxies to investigate the dependence of the
spiral structure on disk parameters and compare the simulation results with the
swing amplification model. We find that the spiral structure in the $N$-body
simulations agrees well with that predicted by the swing amplification for the
wide range of parameters. The pitch angle decreases with increasing the shear
rate and is independent of the disk mass fraction. The number of spiral arms
decreases with both increasing the shear rate and the disk mass fraction. If
the disk mass fraction is fixed, the pitch angle increases with the number of
spiral arms.
