Ariadna Farrés

A dynamical system approach for the station keeping of a solar sail

In this paper we have considered the movement of a solar sail in the Sun-Earth system. As a model we have used the restricted three-body problem adding the solar radiation pressure. It can be seen that we have a two-dimensional family of equilibria parameterized by the two angles defining the sail’s orientation. Most of these equilibrium points are unstable and require a control strategy to keep the sail close to them. We have designed a control strategy that uses the knowledge of the position of the invariant manifolds and how they vary when the sail orientation is changed. We have tested our strategy with two known missions: the Polar Observer and the Geostorm Warning Mission. Simulations of up to 30 years have been performed taking into account errors on the position and velocity determination of the sail and on the sail’s orientation.

Periodic Motion for an Imperfect Solar Sail Near an Asteroid

In this paper we consider the Hill 3-body problem with the extra effect of the solar radiation pressure as a model for the motion of a solar sail close to an asteroid. To model the sail’s acceleration, we include both reflectivity and absorption of the sail’s material. We describe the most relevant dynamical properties of the system for different reflectivity and absorption coefficients as well as different fixed sail orientations. We show families of periodic orbits, describe how they relate to the parameters of the sail and discuss their stability.

On Local Optima in Minimum Time Control of the Restricted Three-Body Problem

The structure of local minima for time minimization in the controlled three-body problem is studied. Several homotopies are systematically used to unfold the structure of these local minimizers, and the resulting singularity of the path associated with the value function is analyzed numerically.

Station Keeping Strategies for a Solar Sail in the Solar System

In this paper we focus on the station keeping around an equilibrium point for a solar sail in the Earth-Sun system. The strategies that we present use the information on the dynamics of the system to derive the required changes on the sail orientation to remain close to an equilibrium point for a long time. We start by describing the main ideas when we consider the RTBP with the effect of the SRP as a model. Then we will see how to extend these ideas when we consider a more complex dynamical model which includes the gravitational attraction of the main bodies in the solar system. One of the goals of the paper is to check the robustness of the algorithms in a more realistic setting and study the effect of errors both in the position determination of the probe and in the orientation of the sail.