Application of the Method of Integral Manifolds for Construction of Resonant Curves for the Problem of Spacecraft Entry into the Atmosphere

The separation of motions into slow (precession) and fast (nutation) components in the problem of the entry of a spacecraft (SC) with a small asymmetry into the atmosphere is considered. For the separation of the slow and fast motions the method of integral manifolds is used together with the asymptotic method for singularly perturbed systems. The separation of motions allows one to isolate the frequencies that are functions of the slow variables of a system, and further on, after determining the integer relations between them, to construct the resonant curves (surfaces). This method gives the possibility to analyze the conditions of the emergence of resonances for a SC at angles of attack that are not small and when aerodynamic characteristics are nonlinear. Examples of the construction of resonant curves for a SC with typical aerodynamic characteristics are considered.