We derive and solve equations, describing in a simplified way the Newtonian dynamics of a self-gravitating nonspherical nonrotating star after its loss of a linear stability, and investigate nonlinear stages of contraction. We find that only pure spherical models can collapse to singularity, but any kind of nonsphericity leads to a dynamic stabilization of the collapse, and formation of regularly or chaotically oscillating body. Therefore nonspherical star without dissipative processes will never reach a singularity. A real collapse happens after damping of the oscillations due to energy losses, shock-wave formation, or viscosity. Detailed analysis of the nonlinear oscillations is performed using a Poincare map construction.
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