Trojan dynamics well approximated by a new Hamiltonian normal form. Issue 2 (28th August 2015)

• Record Type: Journal Article
• Authors: Páez, Rocío Isabel; Locatelli, Ugo
• Is Part Of: Monthly notices of the Royal Astronomical Society. Volume 453:Issue 2(2015)
• Page Start: 2177
• Page End: 2188
• Publication Date: 2015-08-28
• Subjects: celestial mechanics -- planets and satellites: dynamical evolution and stability; Astronomy -- Periodicals; Periodicals; 520.5
• DOI: 10.1093/mnras/stv1792
• Languages: English
• ISSNs: 0035-8711

Abstract

Abstract : We revisit a classical perturbative approach to the Hamiltonian related to the motions of Trojan bodies, in the framework of the planar circular restricted three-body problem, by introducing a number of key new ideas in the formulation. In some sense, we adapt the approach of Garfinkel to the context of the normal form theory and its modern techniques. First, we make use of Delaunay variables for a physically accurate representation of the system. Therefore, we introduce a novel manipulation of the variables so as to respect the natural behaviour of the model. We develop a normalization procedure over the fast angle which exploits the fact that singularities in this model are essentially related to the slow angle. Thus, we produce a new normal form, i.e. an integrable approximation to the Hamiltonian. We emphasize some practical examples of the applicability of our normalizing scheme, e.g. the estimation of the stable libration region. Finally, we compare the level curves produced by our normal form with surfaces of section provided by the integration of the non-normalized Hamiltonian, with very good agreement. Further precision tests are also provided. In addition, we give a step-by-step description of the algorithm, allowing for extensions to more complicated models.