We study the problem of formation shape control under the constraints on the thrust direction. Formations composed of small satellites are usually subject to serious limitations for power consumption, mass, and volume of the attitude and orbit control system (AOCS). If the purpose of the formation flying mission does not require precise tracking of a given relative trajectory, AOCS of satellites may be substantially simplified; however, the capacity of AOCS to ensure a bounded or even periodic relative motion has to be studied first. We consider a formation of two satellites; the deputy one is equipped with a passive attitude control system that provides one‐axis stabilization and a propulsion system that consists of one or two thrusters oriented along the stabilized axis. The relative motion of the satellites is modeled by the Schweighart‐Sedwick linear equations taking into account the effect of J₂ perturbations. We prove that both in the case of passive magnetic attitude stabilization and spin stabilization for all initial relative positions and velocities of satellites there exists a control guaranteeing their periodic relative motion.

This research studies the potential of frozen low lunar orbits to be used in the design of constellations for global and regional communication or navigation. We introduce a robust two-stage approach to the frozen low lunar orbit design based on the successive application of non-gradient techniques, the Bayesian optimization and the Nelder–Mead method. The developed methodology has a number of advantages over existing numerical design techniques and allows revealing orbits with the periodic behavior of the eccentricity vector over long propagation intervals in the full dynamical model. By leveraging a convenient nomogram with constellation visibility parameters and lower bound coverage curves, we have identified most suitable low-altitude orbital configurations of Walker type and then adjust them to be frozen. The frozenness condition can be achieved without changing the orientation of orbital planes. Visibility and coverage metrics (multiplicity of continuous coverage for specified sites, polar regions, or the whole lunar surface; position dilution of precision) of candidate constellations are analyzed. Several promising designs of frozen constellations in near-circular low lunar orbits are singled out. The frozen orbit stability and the station-keeping cost are discussed.