The Symmetrical One-dimensional Newtonian Four-body Problem: A Numerical Investigation |
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Authors: | Winston L. Sweatman |
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Affiliation: | (1) School of Mathematics and Statistics, Napier University, 219, Colinton Road, Edinburgh, EH14 1DJ, Scotland |
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Abstract: | Numerical simulations of the one-dimensional Newtonian four-body problem have been conducted for the special case in which the bodies are distributed symmetrically about the centre of mass. Simulations show a great similarity between this problem and the one-dimensional Newtonian three-body problem. As in that problem the orbits can be divided into three different categories which form well-defined regions on a Poincaré section: there is a region of quasiperiodic orbits about a Schubart-like periodic orbit, there is a region of fast-scattering encounters and in between these two regions there is a chaotic scattering region. The Schubart-like periodic orbit's stability to perturbation is studied. It is apparently stable in one-dimension but is unstable in three-dimensions.This revised version was published online in October 2005 with corrections to the Cover Date. |
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Keywords: | four-body problem collinear motion periodic orbits binary scattering |
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