TITLE:
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DYNAMICS IN THE CENTER MANIFOLD AROUND L2 IN THE QUASI-BICIRCULAR PROBLEM
AUTHOR:
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M.A. ANDREU
Dept. Matematica Aplicada i Analisi, Univ. Barcelona,
Gran Via 585, 08007 Barcelona, Spain.
e-mail: mangel@maia.ub.es
ABSTRACT:
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The Quasi-bicircular problem (QBCP) is a restricted four body problem
where three masses, Earth-Moon-Sun, are revolving in a quasi-bicircular
motion (that is, 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 X center X 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.
KEYWORDS: Four body problem, quasi-bicircular problem, Earth-Moon-Sun system,
center manifold, invariant tori.
To appear in Celestial Mechanics and Dynamical Astronomy.