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math.DS2022★ 7 cited
Determination of the doubly-symmetric periodic orbits in the restricted three-body problem and Hill's lunar problem
Xingbo Xu
We review some recent progress on the research of the periodic orbits of the N-body problem,and propose a numerical scheme to determine the spatial doubly-symmetric periodic orbits…
math.DS2020
Doubly-symmetric periodic orbits in the spatial Hill's lunar problem with oblate secondary primary
Xingbo Xu
In this article we consider the existence of a family of doubly-symmetric periodic orbits in the spatial circular Hill's lunar problem, in which the secondary primary at the origin…
math.DS2015★ 5 cited
Linear stability of the n-gon relative equilibria of the (1+n)-body problem
Xingbo Xu
We consider the linear stabilities of the regular n-gon relative equilibria of the (1+n)-body problem. It is shown that there exist at most two kinds of infinitesimal bodies arrang…