Hamiltonian formulation of the secular theory for Trojan-type motion
Observatoire de la Côte d'Azur, BP 4229, 06304 Nice Cedex 4, France
Accepted: 12 January 2001
We re-derive the secular theory for Trojan-type motion from Morais ([CITE]) using a Hamiltonian formulation and show how this methodology allows us 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.
Key words: celestial mechanics / minor planets, asteroids / planets and satellites: general
© ESO, 2001