On the stability of approximate displaced lunar orbits

In a prior study, a methodology was developed for computing approximate large displaced orbits in the Earth-Moon circular restricted three-body problem (CRTBP) by the Moon-Sail two-body problem. It was found that far from the L(1) and L(2) points, the approximate two-body analysis for large accelerations matches well with the dynamics of displaced orbits in relation to the three-body problem. In the present study, the linear stability characteristics of the families of approximate periodic orbits are investigated

Feedback stabilization of displaced periodic orbits : Application to binary asteroid

This paper investigates displaced periodic orbits at linear order in the circular restricted Earth-Moon system (CRTBP), where the third massless body utilizes a hybrid of solar sail and a solar electric propulsion (SEP). A feedback linearization control scheme is implemented to perform stabilization and trajectory tracking for the nonlinear system. Attention is now directed to binary asteroid systems as an application of the restricted problem. The idea of combining a solar sail with an SEP auxiliary system to obtain a hybrid sail system is important especially due to the challenges of performing complex trajectories

Computer Assisted Proof for Normally Hyperbolic Invariant Manifolds

We present a topological proof of the existence of a normally hyperbolic invariant manifold for maps. In our approach we do not require that the map is a perturbation of some other map for which we already have an invariant manifold. But a non-rigorous, good enough, guess is necessary. The required assumptions are formulated in a way which allows for rigorous computer assisted verification. We apply our method for a driven logistic map, for which non-rigorous numerical simulation in plain double precision suggests the existence of a chaotic attractor. We prove that this numerical evidence is false and that the attractor is a normally hyperbolic invariant curve.Comment: 33 pages, 16 figure

Analysis and control of displaced periodic orbits in the Earth-Moon system

We consider displaced periodic orbits at linear order in the circular restricted Earth-Moon system, where the third massless body is a solar sail. These highly non-Keplerian orbits are achieved using an extremely small sail acceleration. In this paper we will use solar sail propulsion to provide station-keeping at periodic orbits above the L2 point. We start by generating a reference trajectory about the libration points. By introducing a first-order approximation, periodic orbits are derived analytically at linear order. These approximate analytical solutions are utilized in a numerical search to determine displaced periodic orbits in the full nonlinear model. Because of the instability of the collinear libration points, orbit control is needed for a spacecraft to remian in the vicinity of these points. The reference trajectory is then tracked using a linear Quadratic Regulator (LQR). Finally, simulations are given to validate the control strategy. The importance of finding such displaced orbits is to obtain continuous communications between the equatorial regions of the Earth and the polar regions of the Moon

On the stability of displaced two-body lunar orbits

In a prior study, a methodology was developed for computing approximate large displaced orbits in the Earth-Moon circular restricted three-body problem (CRTBP)by the Moon-Sail two-body problem. It was found that far from the L1 and L2 points, the approximate two-body analysis for large accelerations matches well with the dynamics of displaced orbits in relation to the three-body problem. In the present study, the linear stability characteristics of the families of approximate periodic orbits are investigated

Displaced solar sail orbits : dynamics and applications

We consider displaced periodic orbits at linear order in the circular restricted Earth-Moon system, where the third massless body is a solar sail. These highly non-Keplerian orbits are achieved using an extremely small sail acceleration. Prior results have been developed by using an optimal choice of the sail pitch angle, which maximises the out-of-plane displacement. In this paper we will use solar sail propulsion to provide station-keeping at periodic orbits around the libration points using small variations in the sail's orientation. By introducing a first-order approximation, periodic orbits are derived analytically at linear order. These approximate analytical solutions are utilized in a numerical search to determine displaced periodic orbits in the full nonlinear model. Applications include continuous line-of-sight communications with the lunar poles