  Anisotropic cosmological models such as the G\"{o}del universe and its
extensions - G\"{o}del type solutions, are embedded on a visible 3-brane in the
Randall-Sundrum 1 model. The size of the extra dimension is stabilized by
tuning the rotation parameter to a very small value so that hierarchy problem
can be solved. A limiting case also yields the Randall-Sundrum 2 model. The
rotation parameter on the visible brane turns out to be of order $10^{-32}$,
which implies that visible brane essentially lacks rotation.
