Affiliation:
1. School of Science, Hebei University of Technology, Tianjin 300130, China
Abstract
In this paper, we study the existence of the families of odd symmetric periodic solutions in the generalized elliptic Sitnikov (N+1)-body problem for all values of the eccentricity e∈[0,1) using the global continuation method. First, we obtain the properties of the period of the solution of the corresponding autonomous equation (eccentricity e=0) using elliptic functions. Then, according to these properties and the global continuation method of the zeros of a function depending on one parameter, we derive the existence of odd periodic solutions for all e∈[0,1). It is shown that the temporal frequencies of period solutions depend on the total mass λ (or the number N) of the primaries in a delicate way.
Funder
National Natural Science Foundation of China
Natural Science Foundation of Hebei Province
Subject
Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)
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