Abstract
The quasi-bicircular problem (QBCP) is a restricted four body problem where three masses, Earth-Moon-Sun, are revolving in a quasi-bicircular motion (i.e. a coherent motion close to bicircular), the fourth mass being small and not influencing the motion of the three primaries. The QBCP is a Hamiltonian system with three degrees of freedom and depending periodically on time. The L2 point of the QBCP is defined geometrically. It is not an equilibrium point, but there is a small periodic orbit around L2, which has the same stability character center × center × saddle as the L2 libration point of the restricted three body problem (RTBP). The study of orbits around L2 can be useful for the design of future space missions. To give a full description of the different types of orbits in a neighbourhood of L2, it is necessary to skip the hyperbolic part of the Hamiltonian. This is accomplished by the computation of the Hamiltonian reduced to the center manifold around L2 up to high order. The methodology followed for our computations is explained in a general way so it can be applied to any other Hamiltonian system with an equilibrium point having some elliptic and some hyperbolic directions.
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Andreu, M.A. Dynamics in the Center Manifold Around L2 in the Quasi-Bicircular Problem. Celestial Mechanics and Dynamical Astronomy 84, 105–133 (2002). https://doi.org/10.1023/A:1019979414586
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DOI: https://doi.org/10.1023/A:1019979414586