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Classification of periodic orbits in the planar equal-mass four-body problem. (English) Zbl 1360.70017
Summary: 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.

70F10 \(n\)-body problems
70F15 Celestial mechanics
49M15 Newton-type methods
Full Text: DOI
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