On the stability of artificial equilibrium points in the circular restricted three-body problem

This paper investigates new families of displaced, highly non-Keplerian orbits in the two-body problem and artificial equilibria in the circular restricted three-body problem. The families of orbits presented extend prior work by using periodic impulses to generate displaced orbits rather than continuous thrust. The new displaced orbits comprise a sequence of individual Keplerian arcs whose intersection is continuous in position, with discontinuities in velocity removed using impulses. For frequent impulses the new families of orbits approximate continuous thrust non-Keplerian orbits found in previous studies. To generate approximations to artificial equilibria in the circular restricted three-body problem, periodic impulses are used to generate a sequence of connected three-body arcs which begin and terminate at a fixed position in the rotating frame of reference. Again, these families of orbits reduce to the families of artificial equilibria found using continuous thrust.

“…Further investigation of the stability of such artificial equilibria has recently been provided by Bombardelli and Pelaez (2010).…”

Section: Introductionmentioning

confidence: 99%

Displaced non-Keplerian orbits using impulsive thrust

McInnes

2011

“…The topology of such subset of stable AEPs is strictly dependent on the propulsion system type employed by the spacecraft. In fact, as was recently pointed out by Bombardelli and Peláez (2011), if the available propulsive acceleration is low, the stable AEPs are confined to a very restricted region around the classical Lagrange points.…”

Section: Introductionmentioning

confidence: 81%

Artificial equilibrium points for a generalized sail in the circular restricted three-body problem

Aliasi

Mengali

Quarta

2011

This paper introduces a new approach to the study of artificial equilibrium points in the circular restricted three-body problem for propulsion systems with continuous and purely radial thrust. The propulsion system is described by means of a general mathematical model that encompasses the behavior of different systems like a solar sail, a magnetic sail and an electric sail. The proposed model is based on the choice of a coefficient related to the propulsion type and a performance parameter that quantifies the system technological complexity. The propulsion system is therefore referred to as generalized sail. The existence of artificial equilibrium points for a generalized sail is investigated. It is shown that three different families of equilibrium points exist, and their characteristic locus is described geometrically by varying the value of the performance parameter. The linear stability of the artificial points is also discussed.

“…The use of Solar sails to generate non-Keplerian geostationary orbits was considered by Baig and McInnes (2008) and Heiligers et al (2012). Many authors have also established the existence, stability, and controllability conditions of such orbits (McInnes 1977(McInnes , 1998Scheeres 1999;Xu and Xu 2008;Bombardelli and Pelez 2011;Ceriotti et al 2012;Aliasi et al 2012), and recently McKay et al performed a broad survey of NKOs and their utility (McKay et al 2011). Recently, Wang et al offered a new methodology for analysis of the formation flight of electric sails operating in NKOs, and subsequently presented a control framework for such sail formations (Wang et al 2017a, b).…”

Section: Forced Relative Motionmentioning

confidence: 99%

Orbit period modulation for relative motion using continuous low thrust in the two-body and restricted three-body problems

Arnot

McInnes

McKay

et al. 2018

This paper presents rich new families of relative orbits for spacecraft formation flight generated through the application of continuous thrust with only minimal intervention into the dynamics of the problem. Such simplicity facilitates implementation for small, lowcost spacecraft with only position state feedback, and yet permits interesting and novel relative orbits in both two-and three-body systems with potential future applications in space-based interferometry, hyperspectral sensing, and on-orbit inspection. Position feedback is used to modify the natural frequencies of the linearised relative dynamics through direct manipulation of the system eigenvalues, producing new families of stable relative orbits. Specifically, in the Hill-Clohessy-Wiltshire frame, simple adaptations of the linearised dynamics are used to produce a circular relative orbit, frequency-modulated out-of-plane motion, and a novel doubly periodic cylindrical relative trajectory for the purposes of on-orbit inspection. Within the circular restricted three-body problem, a similar minimal approach with position feedback is used to generate new families of stable, frequency-modulated relative orbits in the vicinity of a Lagrange point, culminating in the derivation of the gain requirements for synchronisation of the in-plane and out-of-plane frequencies to yield a singly periodic tilted elliptical relative orbit with potential use as a Lunar far-side communications relay. The v requirements for the cylindrical relative orbit and singly periodic Lagrange point orbit are analysed, and it is shown that these requirements are modest and feasible for existing low-thrust propulsion technology.