In this paper uncontrolled motions of blunt-shaped spacecrafts of small elongation descended in the rarefied atmosphere is considered. Such spacecrafts can have three balancing position of a spatial angle of attack. It can result in a resonance at change of a dynamic pressure at the descend. It is shown, that numerical integration of equations of perturbed motion does not allow to receive authentic results because of stochastic character of transients. Procedure of calculation of the upper and lower estimates of parameters of motion with use of received averaged equations and a stability criteria is developed. Efficiency of this procedure is shown on an example of hypothetical spacecraft descent. The analysis of ways of the resonance elimination is executed. In result, analytical formulas for the initial angular velocity of the spacecraft and for spacecraft’s geometrical parameters are obtained.
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