Skyler Simmons

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20192023

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math.DS2023

The Octahedral Collision-Based Periodic Orbit in the Three-Dimensional Six-Body Problem

Skyler Simmons

We construct a highly-symmetric periodic orbit of six bodies in three dimensions. In this orbit, binary collisions occur at the origin in a regular periodic fashion, rotating betwe…

math.DS2021

The Eight-Body Cubic Collision-Based Periodic Orbit

Skyler Simmons

We construct a highly-symmetric periodic orbit of eight bodies in three dimensions. In this orbit, each body collides with its three nearest neighbors in a regular periodic fashion…

math.DS2019

Stability of Broucke's Isosceles Orbit

Skyler Simmons

We extend the result of Yan to Broucke's isosceles orbit with masses $m_{1}$ , $m_{1}$ , and $m_{2}$ with $2 m_{1} + m_{2} = 3$ . Under suitable changes of variables, isolated binary collisions…