On the stability of the Lagrangian points in the restricted circular 3-body problem

Abstract

[en] The 3-body problem is one of the most celebrated problems in mathematics. In this work we aim to find the equilibrium points of one of the three masses, which is considered infinitesimal, and study their stability in two different phase spaces. The question of stability is addressed using both analytical and numerical methods. Whereas the Lyapunov and KAM theories provide us with analytical proofs of the stable or unstable behaviour in the first phase space, analytical methods motivated by the Nekhoroshev theory allow us to compute practical bounds of the time until which the infinitesimal mass remains near the equilibria in the second. Finally, these bounds are applied to the case of a well known system: the Sun-Jupiter-Trojan system.