J.Cusco: "“Computation of the Centre Manifold of a Solar Sail Periodic Orbit”

A Solar sail is a spacecraft endowed with a large and highly reflecting surface
to take advantage of the solar radiation pressure to propel the spacecraft.
In this work we focus on the motion of a solar sail in the Earth-Moon system. The
model used is a coherent version of the Bicircular Problem extended to include the effect
of the Solar Radiation Pressure on the sail. This model can be regarded as a periodic
time-dependent perturbation of the well-known Restricted Three Body Problem. This
system can be written in Hamiltonian form as a three and a half degrees of freedom. Thus,
the classical Lagrangian points are no longer equilibria but they are replaced by periodic
orbits with the same period as the time-dependence. The model has three parameters: one
of them describes the performance of the sail and the other two describe its orientation.
This leads to a three-parametric family of periodic orbits that raise from each Lagrangian
point.
We focus in a periodic orbit near the point L2. Then we perform a partial normal form
process to the Hamiltonian function to obtain a new autonomous Hamiltonian that has
uncoupled elliptic and hyperbolic parts. Therefore, we can reduce the study of the motion
near the periodic orbit to the study of a two degrees of freedom autonomous Hamiltonian
system and, by fixing some section and energy level, to the study of a family of Area
Preserving Maps.
Joint work with Ariadna Farr´es and Angel Jorba.