Chaotic Motion of a Reentry Capsule During Descent into the Atmosphere

Conical-shaped reentry capsules with a spherical bottom and a displaced center of mass from the axis of symmetry are widely used in astronautics for payload delivery. In the case of control-system breakage, modern reentry capsules allow a successful landing to be carried out in an uncontrolled mode. At the same time, the aerodynamic features of this particular shape create preconditions for chaotic motion. This can lead to an overturn of the capsule, thus creating the risk of an accident. This article explores uncontrolled descent of the reentry capsule, with slight asymmetry, into the atmosphere. The system of differential equations describing uncontrollable descent of an asymmetric capsule in the atmosphere was recorded. Fast and slow variables were introduced. A simplified system of equations was obtained, describing the change of the spatial angle of attack. It was shown that chaotic motion can occur during the uncontrolled descent in the atmosphere. The algorithm of damping coefficient selection was developed on the basis of Melnikov’s method. Its application allows for the elimination of chaos in the whole descent trajectory, thus increasing the system reliability.