Asymptotic Analysis of the Stability of the Angle of Attack in an Atmospheric Descent of a Spacecraft with Small Mass and Inertial Asymmetries

We consider the problem of an uncontrolled descent of a spacecraft with a small asymmetry in a low-density atmosphere with small values of the angle of attack. The aim of this study is to obtain the stability conditions for the angle of attack of a spacecraft with small mass and inertial asymmetries, descending in a low-density atmosphere. The motion of the spacecraft relative to its center of mass is described by a nonlinear low-frequency dynamical system. We linearize the low-frequency system, taking into account the small values of the angle of attack. The application of the averaging method makes it possible to substantially simplify the linearized equations and to obtain an approximate analytical stability condition for the angle of attack. The reliability of the obtained stability condition is confirmed by the results of numerical integration of the equation for the angle of attack.