# Periodic Solutions for Circular Restricted 4-body Problems with Newtonian Potentials

@article{Zhao2013PeriodicSF, title={Periodic Solutions for Circular Restricted 4-body Problems with Newtonian Potentials}, author={Xiaoxia Zhao and Shiqing Zhang}, journal={arXiv: Mathematical Physics}, year={2013} }

We study the existence of non-collision periodic solutions with Newtonian potentials for the following planar restricted 4-body problems: Assume that the given positive masses $m_{1},m_{2},m_{3}$ in a Lagrange configuration move in circular obits around their center of masses, the sufficiently small mass moves around some body. Using variational minimizing methods, we prove the existence of minimizers for the Lagrangian action on anti-T/2 symmetric loop spaces. Moreover, we prove the minimizers…

## 2 Citations

### Periodic Solutions for Circular Restricted N + 1-Body Problems

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and Applied Analysis 3 the critical point of f(q) in Λ ± is a periodic solution of Newtonian equation (5). Lemma 11. (1) (Gordon’s theorem [19]) Let x ∈ W 1,2 ([t 1 , t 2 ], R K ) and x(t 1 ) = x(t 2…

### Periodic Solutions for Circular Restricted -Body Problems

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For circular restricted -body problems, we study the motion of a sufficiently small mass point (called the zero mass point) in the plane of equal masses located at the vertices of a regular polygon.…

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