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Noncollision Periodic Solutions for Circular Restricted Planar Newtonian Four-Body Problems

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  • Xiaoxiao Zhao

    (School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China)

  • Liang Ding

    (School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang 550025, China)

  • Shiqing Zhang

    (Yangtze Center of Mathematics and College of Mathematics, Sichuan University, Chengdu 610064, China)

Abstract

We study a class of circular restricted planar Newtonian four-body problems in which three masses are positioned at the vertices of a Lagrange equilateral triangle configuration, each mass revolving around the center of mass in circular orbits. Assuming that the value of the fourth mass is negligibly small (i.e., it does not perturb the motion of the other three masses, though its own motion is influenced by them), we use variational minimization methods to prove the existence of noncollision periodic solutions with some fixed winding numbers. These noncollision solutions exist for both equal and unequal mass values for the three bodies located at the vertices of the Lagrange equilateral configuration.

Suggested Citation

  • Xiaoxiao Zhao & Liang Ding & Shiqing Zhang, 2025. "Noncollision Periodic Solutions for Circular Restricted Planar Newtonian Four-Body Problems," Mathematics, MDPI, vol. 13(18), pages 1-14, September.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:18:p:3015-:d:1752180
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