A class of periodic solutions of the N-body problem

Details A class of periodic solutions of the N-body problem A class of periodic solutions of the N-body problem

Jun 1989

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989cemda..46..177z&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 46, Issue 2, pp.177-186

Astronomy and Astrophysics

Astronomy

1

Scientific paper

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 ɛα2,...,∈α N , ɛ small. We find solutions such that the body of mass 1 moves close to x = 0 while the body of mass ɛαi 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.

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