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

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.

Reorientation of Asymmetric Rigid Body Using Two Controls

Most spacecrafts are designed to be maneuvered to achieve pointing goals. This is accomplished usually by designing a three-axis control system, which can achieve arbitrary maneuvers, where the goal is to repoint the spacecraft and match a desired angular velocity at the end of the maneuver. New control laws are required, however, if one of the three-axis control actuators fails. This paper explores suboptimal maneuver strategies when only two control torque inputs are available. To handle this underactuated system control problem, the three-axis maneuver strategy is transformed to two successive independent submaneuver strategies. The first maneuver is conducted on one of the available torque axes. Next, the second maneuver is conducted on the torque available plane using two available control torques. However, the resulting control law is more complicated than the general three-axis control law. This is because an optimal switch time needs to be found for determining the end time for the single-axis maneuver or the start time for the second maneuver. Numerical simulation results are presented that compare optimal maneuver strategies for both nominal and failed actuator cases.