Natural periodic orbit-attitude behaviors for rigid bodies in three-body periodic orbits

Abstract

Trajectory design increasingly leverages multi-body dynamical structures that are based on an understanding of various types of orbits in the Circular Restricted Three-Body Problem (CR3BP). Given the more complex dynamical environment, mission applications may also benefit from deeper insight into the attitude motion. In this investigation, the attitude dynamics are coupled with the trajectories in the CR3BP. In a highly sensitive dynamical model, such as the orbit-attitude CR3BP, periodic solutions allow delineation of the fundamental dynamical structures. Periodic solutions are also a subset of motions that are bounded over an infinite time-span (assuming no perturbing factors), without the necessity to integrate over an infinite time interval. Euler equations of motion and quaternion kinematics describe the rotational behavior of the spacecraft, whereas the translation of the center of mass is modeled in the CR3BP equations. A multiple shooting and continuation procedure is employed to target orbit-attitude periodic solutions in this model. Application of Floquet theory and Poincaré mappings to identify initial guesses for the targeting algorithm are described. In the Earth–Moon system, representative scenarios are explored for axisymmetric vehicles with various inertia characteristics, assuming that the vehicles move along L1/L2 Lyapunov orbits as well as distant retrograde orbits. A rich structure of possible periodic behaviors appears to pervade the solution space in the coupled problem. The stability analysis of the attitude dynamics for the available families is included. Among the computed solutions, marginally stable and slowly diverging rotational behaviors exist and may offer interesting mission applications.