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Invariant manifolds of a non-autonomous quasi-bicircular problem computed via the parameterization method

Le Bihan, Bastien and Masdemont, Josep and Gómez, Gérard and Lizy-Destrez, Stéphanie Invariant manifolds of a non-autonomous quasi-bicircular problem computed via the parameterization method. (2017) Nonlinearity, 30 (8). 3040-3087. ISSN 0951-7715

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Official URL: https://doi.org/10.1088/1361-6544/aa7737

Abstract

The parameterization method (pm) has been used to compute high-order parameterizations of invariant manifolds of vector fields at xed points. This paper extends such approach to invariant manifolds of periodically-perturbed vector fields about a periodic orbit with the same frequency, with a direct application on the libration points of the Sun-Earth-Moon system. The Sun-Earth-Moon environment is modeled by the so-called Quasi-Bicircular Model (qbcp), which is a coherent restricted four-body model that describes the motion of a spacecraft under the simultaneous gravitational influences of the Earth, the Moon, and the Sun. The pm is adapted to account for the explicit time-dependency of the corresponding vector field. This new procedure yields high-order periodic semi-analytical approximations of the center manifolds about the libration points L1;2 of the periodically-perturbed Sun-(Earth+Moon) and Earth-Moon systems. These approximations are then used to initialize the computation of Poincaré maps, which allow to get a qualitative description of the non-autonomous dynamics near the equilibrium points. It is shown that, with this new approach, the semi-analytical description of the center manifolds in a coherent four-body environment is valid in a neighborhood significant enough to be used in practice. In particular, the well-known Halo orbit bifurcation is recovered in all cases.

Item Type:Article
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Other partners > Universitat Politècnica de Catalunya - UPC (SPAIN)
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Deposited By: Lizy-Destrez Stéphanie
Deposited On:13 Nov 2018 14:21

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