We consider the periodic problem for a class of planar N-body systems in Celestial Mechanics, Our goal is to give a variational characterization of the Hill's (retrograde) orbits as minima of the action functional under some geometrical and topological constraints. The method developed here also turns out to be useful in the study of the full problem with N primaries each having at most two satellites
Arioli, G., Gazzola, F., Terracini, S. (2000). Minimization properties of Hill's orbits and applications to some $N$-body problems. ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE, 17(5), 617-650 [10.1016/S0294-1449(00)00122-0].
Minimization properties of Hill's orbits and applications to some $N$-body problems
Terracini, S
2000
Abstract
We consider the periodic problem for a class of planar N-body systems in Celestial Mechanics, Our goal is to give a variational characterization of the Hill's (retrograde) orbits as minima of the action functional under some geometrical and topological constraints. The method developed here also turns out to be useful in the study of the full problem with N primaries each having at most two satellites
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