Classification of periodic orbits in the planar equal-mass four-body problem

Duokui  Yan; Tiancheng Ouyang; Zhifu Xie

doi:10.3934/proc.2015.1115

Article Contents

2015, Volume 2015: 1115-1124. Doi: 10.3934/proc.2015.1115 open access

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Classification of periodic orbits in the planar equal-mass four-body problem

1.
School of Mathematics and System Science, Beihang University, Beijing 100191
2.
Department of Mathematics, Brigham Young University, Provo, Utah 84602
3.
Department of Mathematics and Computer Science, Virginia State University, Petersburg, Virginia 23806

Received: September 2014

Revised: April 2015

Published: November 2015

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Abstract

In the N-body problem, many periodic orbits are found as local Lagrangian action minimizers. In this work, we classify such periodic orbits in the planar equal-mass four-body problem. Specific planar configurations are considered: line, rectangle, diamond, isosceles trapezoid, double isosceles, kite, etc. Periodic orbits are classified into 8 categories and each category corresponds to a pair of specific configurations. Furthermore, it helps discover several new sets of periodic orbits.

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Mathematics Subject Classification: Primary: 70F10, 70F15; Secondary: 49M15.

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References

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