  We study the complete evolution of a flat and homogeneous universe dominated
by tachyonic matter. We demonstrate the attractor behaviour of the tachyonic
inflation using the Hamilton-Jacobi formalism. We else obtain analytical
approximations to the trajectories of the tachyon field in different regions.
The numerical calculation shows that an initial non-vanishing momentum does not
prevent the onset of inflation. The slow-rolling solution is an attractor.
