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Trojan dynamics well approximated by a new Hamiltonian normal form | | Rocio Isabel Paez
; Ugo Locatelli
; | | Date: |
3 Aug 2015 | | 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 (PCRTBP), by introducing a number of key new
ideas 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 accurate
representation of the system. Therefore, we introduce a novel manipulation of
the variables so as to respect the natural behavior 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. | | Source: | arXiv, 1508.0381 | | Services: | Forum | Review | PDF | Favorites | |
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