The chaotic analysis of movement of the spacecraft with small mass asymmetry at descent in an atmosphere

The uncontrolled motion of the spacecraft with small mass asymmetry at descent in atmosphere is investigated by the methods of chaotic dynamics. The restoring moment acts on the spacecraft. It approximated by biharmonic expression. With the help of Melnikov method the behaviour of a system in neighbourhood of the separatrix is investigated. Analytical solutions for homoclinic trajectories are received. Criteria of occurrence of chaos are found. The results of the numerical modelling are show validity of received solutions. Change of thickness of a chaotic layer is investigated during descent of the spacecraft at atmosphere. Recommendations are given at the choice of the damping eliminating a capability of occurrence of chaotic transitions on all trajectory of descent.