A new collision-based periodic orbit in the three-dimensional eight-body problem

S Simmons - Celestial Mechanics and Dynamical Astronomy, 2022 - Springer
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 …

[HTML][HTML] A separating surface for Sitnikov-like n+ 1-body problems

L Bakker, S Simmons - Journal of Differential Equations, 2015 - Elsevier
We consider the generalized Sitnikov problem of Newtonian mechanics. For periodic, planar
configurations of n bodies which are symmetric under rotation by a fixed angle, the z-axis is …

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

S Simmons - arXiv preprint arXiv:2308.11625, 2023 - arxiv.org
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 between pairs of …

Stability of Broucke's isosceles orbit

S Simmons - arXiv preprint arXiv:1903.08981, 2019 - arxiv.org
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 …

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

S Simmons - 2023 - researchsquare.com
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 between pairs of …

Central Configurations and Action Minimizing Orbits in Kite Four‐Body Problem

B Benhammouda, A Mansur, M Shoaib… - Advances in …, 2020 - Wiley Online Library
In the current article, we study the kite four‐body problems with the goal of identifying global
regions in the mass parameter space which admits a corresponding central configuration of …

The Eight-Body Cubic Collision-Based Periodic Orbit

S Simmons - arXiv preprint arXiv:2110.06174, 2021 - arxiv.org
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 …

[PDF][PDF] Central configurations in the general four body coplanar problem with different masses

M Shoaib, B Benhammouda, BA Steves, WL Sweatman - 2023 - researchgate.net
A generic method for finding central configurations in the general four body coplanar
problem with four different masses is derived. New families of non-symmetrical central …

[图书][B] Analysis of Multiple Collision-Based Periodic Orbits in Dimension Higher than One

SC Simmons - 2015 - search.proquest.com
We exhibit multiple periodic, collision-based orbits of the Newtonian n-body problem. Many
of these orbits feature regularizable collisions between the masses. We demonstrate …