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 …
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 …
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 …
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 …
$ 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 …
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
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 …
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 …
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
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 …
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 …
of these orbits feature regularizable collisions between the masses. We demonstrate …