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We revisit a classical perturbative approach to the Hamiltonian related tothe motions of Trojan bodies, in the framework of the Planar CircularRestricted Three-Body Problem (PCRTBP), by introducing a number of key newideas in the formulation. In some sense, we adapt the approach of Garfinkel(1977) to the context of the normal form theory and its modern techniques.First, we make use of Delaunay variables for a physically accuraterepresentation of the system. Therefore, we introduce a novel manipulation ofthe variables so as to respect the natural behavior of the model. We develop anormalization procedure over the fast angle which exploits the fact thatsingularities in this model are essentially related to the slow angle. Thus, weproduce a new normal form, i.e. an integrable approximation to the Hamiltonian.We emphasize some practical examples of the applicability of our normalizingscheme, e.g. the estimation of the stable libration region. Finally, we comparethe level curves produced by our normal form with surfaces of section providedby the integration of the non--normalized Hamiltonian, with very goodagreement. Further precision tests are also provided. In addition, we give astep-by-step description of the algorithm, allowing for extensions to morecomplicated models.

Trojan dynamics well approximated by a new Hamiltonian normal form