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 epsilon alpha(2), ... , epsilon alpha(N), epsilon small. We find solutions such that the body of mass 1 moves close to x = 0 while the body of mass epsilon alpha(i) moves close to one of the circular solutions of the two body problem of period T/k(i), where k(i) is any odd number. No relation has to be satisfied by k(2), ... , k(N).
A Class of Periodic Solutions of the N-body Problem / COTI ZELATI, Vittorio. - In: CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY. - ISSN 0923-2958. - STAMPA. - 46:(1989), pp. 177-186. [10.1007/BF00053047]
A Class of Periodic Solutions of the N-body Problem
COTI ZELATI, VITTORIO
1989
Abstract
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 epsilon alpha(2), ... , epsilon alpha(N), epsilon small. We find solutions such that the body of mass 1 moves close to x = 0 while the body of mass epsilon alpha(i) moves close to one of the circular solutions of the two body problem of period T/k(i), where k(i) is any odd number. No relation has to be satisfied by k(2), ... , k(N).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.