About the Attractor-Repeller points during the descent of an asymmetric spacecraft in the atmosphere

The aim of this study is to analyze the resonant attractor-repeller points during the atmospheric descent of a spacecraft with small asymmetry. The mathematical simulation of spacecraft rotational motion uses an approximate non-linear system of equations obtained by the method of integral manifolds. Application of the averaging method and the Lyapunov method makes it possible to obtain realization conditions of attractor-repeller points on non-resonance parts of the motion. By analyzing of the said conditions, we have identified specific cases when the principal resonance is either an attractor point or a repeller point.