Àngel Jorba

Study of the transfer from the Earth to a halo orbit around the equilibrium pointL 1

The purpose of this paper is to study a transfer strategy from the vicinity of the Earth to a halo orbit around the equilibrium pointL1 of the Earth-Sun system. The study is done in the real solar system (we use the DE-118 JPL ephemeris in the simulations of motion) although some simplified models, such as the restricted three body problem (RTBP) and the bicircular problem, have been also used in order to clarify the geometrical aspects of the problem. The approach used in the paper makes use of the hyperbolic character of the halo orbits under consideration. The invariant stable manifold of these orbits enables the transfer to be achieved with, theoretically, only one manoeuvre: the one of insertion into the stable manifold. For the total Δv required, the figures obtained are similar to the ones given by the standard procedures of optimization.

On quasi-periodic perturbations of elliptic equilibrium points

This work focuses on quasi-periodic time-dependent perturbations of ordinary differential equations near elliptic equilibrium points. This means studying \[ \dot x = (A + \varepsilon Q(t,\varepsilon ))x + \varepsilon g(t,\varepsilon ) + h(x,t,\varepsilon ), \] where A is elliptic and h is

On the reducibility of linear differential equations with quasiperiodic coefficients

\mathcal{O}(x^2 )

The Bicircular Model Near the Triangular Libration Points of the RTBP

. It is shown that, under suitable hypothesis of analyticity, nonresonance and nondegeneracy with respect to

STUDY OF THE TRANSFER BETWEEN HALO ORBITS

\varepsilon

A dynamical equivalent to the equilateral libration points of the Earth-Moon system

, there exists a Cantorian set

Lindstedt Series for Lower Dimensional Tori

\mathcal{E}

Effective Stability for Periodically Perturbed Hamiltonian Systems

such that for all

Review of general and Toeplitz vector bidiagonal solvers

\varepsilon \in \mathcal{E}

Splitting of separatrices for (fast) quasiperiodic forcing

there exists a quasi-periodic solution such that it goes to zero when