Linear Stability for Some Symmetric Periodic Simultaneous Binary Collision Orbits in the Four-Body Problem

Abstract

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 body problem with masses 1, m, m, 1, and also in a symmetric planar four-body problem with equal masses. For the collinear problem, this verifies the earlier numerical results of Sweatman for linear stability.

16 pages, 4 figures

References in corpus (3)

• Chaos in the one-dimensional gravitational three-body problem
• Existence and Stability of Symmetric Periodic Simultaneous Binary Collision Orbits in the Planar Pairwise Symmetric Four-Body Problem
• Periodic Solutions with Singularities in Two Dimensions in the $n$-body Problem

Cited by in corpus (5)

• Existence and Stability of Symmetric Periodic Simultaneous Binary Collision Orbits in the Planar Pairwise Symmetric Four-Body Problem
• Periodic Solutions with Singularities in Two Dimensions in the $n$-body Problem
• Linear Stability Analysis of Symmetric Periodic Simultaneous Binary Collision Orbits in the Planar Pairwise Symmetric Four-Body Problem
• A Separating Surface for Sitnikov-like n+1-body Problems
• The Eight-Body Cubic Collision-Based Periodic Orbit