The N-body problem
Féjoz, Jacques (2015), The N-body problem, in Alessandra Celletti, Celestial Mechanics, Unesco : Paris, p. 126-167
External document linkhttps://www.ceremade.dauphine.fr/~fejoz/Articles/Fejoz_2014_nbp.pdf
Book titleCelestial Mechanics
Book authorAlessandra Celletti
Series titleEncyclopedia of Life Support Systems
Number of pages520
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CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Institut de Mécanique Céleste et de Calcul des Ephémérides [IMCCE]
Abstract (EN)We introduce the N-body problem of mathematical celestial mechanics, and discuss its astronomical relevance, its simplest solutions inherited from the two-body problem (called homographic motions and, among them, homothetic motions and relative equilibria), Poincaré's classification of periodic solutions, symmetric solutions and in particular choreographies such as the figure-eight solution, some properties of the global evolution and final motions, Chazy's classification in the three-body problem, some non-integrability results, perturbations series of the planetary problem and a short account on the question of its stability.
Subjects / KeywordsNewton's equation; symmetry; reduction; Conley-Wintner endomorphism; stability; planetary problem; Hill's problem; central configuration; homographic motions; relative equilibria; homothetic motion; periodic orbit; Poincaré's classification; choreography; figure-eight solution; Lagrangian action; Lagrange-Jacobi identity; Sundman's inequality; collision; regularization; Marchal-Chenciner's theorem; non-collision singularity; final motions; Chazy's classification; integrability; first integral; transverse heteroclinic intersection; monodromy group; differential Galois theory; Lindstedt series; von Zeipel series; small denominators; Birkhoff series; Lagrange and Laplace stability theorems; Arnold's theorem; quasi-periodic orbit; Nekhoroshev theorem; KAM theory; instability; symbolic dynamics
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