We investigated dynamical collapse of a molecular cloud core with three-dimensional numerical simulations. Our simulations show that an initially spherical core produces a bar or disk during its dynamical collapse. The disk and bar formation are due to instability. Velocity perturbations grow in proportion to where denotes the central density. The growing velocity perturbations are due to two effects, rotation and shear.
Rotation makes the core spin faster to produce a disk at the center.
On the other hand, velocity shear elongates or shortens the core in one direction to form a bar or non-rotating disk. When the core rotates non-uniformly, the collapse produces a disk containing a bar at its center by the growth of rotation and shear. This bar is much longer than the Jeans length and is likely to be unstable against fragmentation. We expect that the bar will evolve into a binary or multiple stars. The binary or multiple stars will be surrounded by a common disk.