Minimization properties of Hill's orbits and applications to some \(N\)-body problems

DOI10.1016/S0294-1449(00)00122-0zbMath0977.70006MaRDI QIDQ1590095

Susanna Terracini, Gianni Arioli, Gazzola, Filippo

Publication date: 12 March 2001

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIHPC_2000__17_5_617_0

zbMATH Keywords

periodic problemHill's orbitsminima of action functionalnon-collision orbitsplanar \(N\)-body systems

Mathematics Subject Classification ID

Celestial mechanics (70F15) (n)-body problems (70F10)

Related Items (11)

Variational existence proof for multiple periodic orbits in the planar circular restricted three-body problem ⋮ Periodic solutions for planar four-body problems ⋮ Existence and uniqueness result for a fluid-structure-interaction evolution problem in an unbounded 2D channel ⋮ On the variational approach to the periodic \(n\)-body problem ⋮ New periodic solutions for planar five-body and seven-body problems ⋮ New periodic solutions for 2\(n\)-body problems in \(R^{3}\) ⋮ Rose solutions with three petals for planar 4-body problems ⋮ Entire minimal parabolic trajectories: the planar anisotropic Kepler problem ⋮ New periodic solutions for some planar \(N + 3\)-body problems with Newtonian potentials ⋮ New periodic solutions for planar \((N+2)\)-body problems ⋮ Variational proof of the existence of periodic orbits in the spatial Hill problem and its constrained problems

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