Hamiltonian formulation of the secular theory for Trojan-type motion

We re-derive the secular theory for Trojan-type motion from Morais (1999) using a Hamiltonian formulation and show how this methodology allows up to include the effect of an oblate central mass and the secular perturbations from additional bodies in a rigorous way. As an application of this work we locate secular resonances inside the co-orbital regions of the uranian satellites and the planets, and show that these are in good agreement with the behaviour observed in numerical integrations.