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A class of periodic solutions of the N-body problem

Zelati, Vittorio Coti (1989), A class of periodic solutions of the N-body problem, Celestial Mechanics and Dynamical Astronomy, 46, 2, p. 177-186. http://dx.doi.org/10.1007/BF00053047

Type
Article accepté pour publication ou publié
Date
1989
Journal name
Celestial Mechanics and Dynamical Astronomy
Volume
46
Number
2
Publisher
Springer
Pages
177-186
Publication identifier
Metadata
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Author(s)
Zelati, Vittorio Coti
Abstract (EN)
We prove existence and multiplicity of T-periodic solutions (for any given T) for the N-body problem in ℝ m (any m ⩾ 2) where one of the bodies has mass equal to 1 and the others have masses εα2,...,∈α N , ε small. We find solutions such that the body of mass 1 moves close to x = 0 while the body of mass εαi moves close to one of the circular solutions of the two body problem of period T/k i, where ki is any odd number. No relation has to be satisfied by k 2,...,k N.
Subjects / Keywords
N-body problem