Chaotic motion of a body of the blunted form in an atmosphere described is considered by the nonlinear differential equation of the second order. On a body the restoring moment, the small perturbed periodic moment and the damped moment operates. The phase portrait of the unperturbed system has points of unstable balance. On the basis of Melnikov method the criteria determining borders of chaos of system are found. The results of the numerical simulations confirming validity, received criterion are submitted.
