28 citations · 56 across the 7 of their papers we have counts for
9 papers
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…
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…
Stability of Broucke's Isosceles Orbit
Skyler Simmons
We extend the result of Yan to Broucke's isosceles orbit with masses , , and with . Under suitable changes of variables, isolated binary collisions…
A Separating Surface for Sitnikov-like n+1-body Problems
Lennard Bakker, Skyler Simmons
We consider the restricted n + 1-body problem of Newtonian mechanics. For periodic, planar configurations of n bodies which is symmetric under rotation by a fixed angle, the z-axis…
Stability of the Rhomboidal Symmetric-Mass Orbit
Lennard Bakker, Skyler Simmons
We study the rhomboidal symmetric-mass 4-body problem in both a two-degree-of-freedom and a four-degree-of-freedom setting. Under suitable changes of variables in both settings, is…
Linear Stability Analysis of Symmetric Periodic Simultaneous Binary Collision Orbits in the Planar Pairwise Symmetric Four-Body Problem
Lennard F. Bakker, Scott C. Mancuso, Skyler C. Simmons
We apply the symmetry reduction method of Roberts to numerically analyze the linear stability of a one-parameter family of symmetric periodic orbits with regularizable simultaneous…
Existence and Stability of Symmetric Periodic Simultaneous Binary Collision Orbits in the Planar Pairwise Symmetric Four-Body Problem
Lennard F. Bakker, Tiancheng Ouyang, Duokui Yan +1
We extend our previous analytic existence of a symmetric periodic simultaneous binary collision orbit in a regularized fully symmetric equal mass four-body problem to the analytic…
Linear Stability for Some Symmetric Periodic Simultaneous Binary Collision Orbits in the Four-Body Problem
Lennard F. Bakker, Tiancheng Ouyang, Skyler Simmons +2
We apply the analytic-numerical method of Roberts to determine the linear stability of time-reversible periodic simultaneous binary collision orbits in the symmetric collinear four…
Periodic Solutions with Singularities in Two Dimensions in the -body Problem
Tiancheng Ouyang, Skyler C. Simmons, Duokui Yan
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 use…