  We perform N-body simulations of the dynamical evolution of a dwarf galaxy
falling into the Milky Way galaxy in order to understand the formation scenario
of the peculiar globular cluster $\omega$ Centauri. We use self-consistent
models of the bulge and the disc of the Milky Way, as well as of the dwarf
galaxy, and explore a range of dwarf models with different density
distributions. Namely, we use King (1966) and Hernquist (1990) density profiles
to model the density distribution in the dwarf. The central region of our King
model has a density profile approximately $\propto r^{-2}$, while that of the
Hernquist model is $\propto r^{-1}$. The difference in the dwarf's density
distributions leads to distinct evolutionary scenarios. The King model dwarf
loses its mass exponentially as a function of apocentric distance, with the
mass-loss rate depending on the initial mass and size of the dwarf. Regardless
of the initial mass and size, the King model dwarf remains more massive than
$10^8$ \msun after a few Gyr of evolution. The Hernquist model dwarf
experiences an accelerated mass loss, and the mass of the remnant falls below
$10^8$ \msun within a few Gyr. By exploring an appropriate set of parameters,
we find a Hernquist model that can attain the mass and orbital characteristics
of $\omega$ Cen after a few Gyr.
