Periodic Solutions with Singularities in Two Dimensions in the $n$-body Problem

Mathematics – Dynamical Systems

Scientific paper

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Scientific paper

Analytical methods are used to prove the existence of a periodic, symmetric
solution with singularities in the planar 4-body problem. A numerical
calculation and simulation are used to generate the orbit. The analytical
method easily extends to any even number of bodies. Multiple simultaneous
binary collisions are a key feature of the orbits generated.

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