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

Xiaoxiao Zhao (), Liang Ding and Shiqing Zhang ()
Additional contact information
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

Mathematics, 2025, vol. 13, issue 18, 1-14

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.

Keywords: planar Newtonian four-body problems; noncollision periodic solutions; circular orbits; variational minimizers; winding numbers (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/18/3015/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/18/3015/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:18:p:3015-:d:1752180

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().