Estimation of the probability of two consecutive passages through resonance during the descent of an asymmetric rigid body in a rarefied atmosphere

Abstract

A two-frequency nonlinear system of ordinary differential equations is considered. This system describes the perturbed motion of a rigid body with considerable asymmetry in a rarefied atmosphere. It is known that when the frequencies of this system of equations coincide, the phenomena of capture or passage through the principal resonance, which have a random nature, are possible. In this case, the probability of a passage through the resonance is calculated from the initial conditions on the separatrix. The objective of this study is to obtain an expression for estimating the probability of two consecutive passages through the resonance regions during the descent in the rarefied atmosphere of Mars of a rigid body with significant geometric and aerodynamic asymmetry.