Dynamic stabilization of L2 periodic orbits using attitude-orbit coupling effects

Abstract

Numerical explorations show how the known periodic solutions of the Hill problem are modified in the case of the attitude-orbit coupling that may occur for large satellite structures. We focus on the case in which the elongation is the dominant satellite's characteristic and find that a rotating structure may remain with its largest dimension in a plane parallel to the plane of the primaries. In this case, the effect produced by the non-negligible physical length is dynamically equivalent to the perturbation produced by an oblate central body on a mass-point satellite. Based on this, it is demonstrated that the attitude-orbital coupling of a long enough body may change the dynamical characteristics of a periodic orbit about the collinear Lagrangian points.

Minimum Time Control of the Rocket Attitude Reorientation Associated with Orbit Dynamics

“…Numerical simulations show that the initialization step for the direct method procedure is quite robust (a constant initial guess is enough). The results are reported on Figures 12,13 and 14. We observe that, when t ∈ [23,43], the control oscillates much with a modulus less than 1: this indicates that there is a singular arc in the "true" optimal trajectory, and therefore chattering Note that, along the singular arc, the variables ω x , ω y , p ωx , p ωy , p θ , p ψ and p φ are almost equal to 0, and we check that this arc indeed lives on the singular surface S defined by (26). Therefore, it turns out that there is a singular arc in the optimal trajectory, causing chattering at the junction with regular arcs.…”

“…However, for the rockets, the trajectory is controlled by its attitude angles: the way to make the rocket follow its nominal trajectory is to change its attitude angles, and therefore it is desirable to be able to determine the optimal control subject to the coupled dynamical system. Though the control of the coupled problem was also studied in many previous works (see, e.g., [23,17,20]), it does not seem that the problem has been investigated in the optimal control framework so far.…”

The spatial Hill four-body problem I -- An exploration of basic invariant sets

“…The members of this family possess symmetry of type III. In the H3BP, it was found [45] that the size of these eight shaped orbits increases as the value of C decreases monotonically; this behaviour stands even when C → −∞. All orbits are unstable and there is just one critical spatial orbit for C = 0.512431.…”

“…Furthermore, the author made the conjecture: the orbits tend asymptotically towards a rectilinear collision motion on the half-axis x = y = 0, z ≤ 0. Further explorations, as the contained in [45], provide data about the stability of this family; almost all orbits within the family are unstable except in a short region of C with length ∆C = 0.02612.…”

Attitude Responses in Coupled Orbit-Attitude Dynamical Model in Earth–Moon Lyapunov Orbits

“…Recent investigations have examined the motion of a spacecraft located in various two-and three-dimensional periodic reference orbits, in the vicinity of the Earth-Moon collinear libration points. Lara et al numerically investigate the attitude-orbit coupling of a large dumbbell satellite on halo and vertical L 2 orbits in the Hill problem [9]. If the spacecraft is in fast rotation and the equations of motion are averaged over the "fast" angle, the attitude dynamics of the dumbbell decouple from the orbital motion and the orbital dynamics simplify [10].…”