Stabilizing Chaos in the Four-Body Problem: Alp's Elastic Dark Matter vs Newtonian Dynamics

"This is an updated version with corrected simulation parameters, improved figures, and detailed interpretation." The four-body problem, a cornerstone of celestial mechanics, is notoriously sensitive to initial conditions and often leads to chaotic motion. We investigate a novel stabilization mechanism using the AlpsElastic Dark Matter (AEDM) model, which introduces an elastic force in addition to Newtonian gravity. By numerically integrating the system over 30 days and analyzing total energy, angular momentum,orbital structure, and frequency spectra, we demonstrate that the AEDM model suppresses chaos andestablishes bounded quasi-periodic motion. A comparison with the purely Newtonian model reveals thestabilizing effect of elasticity in complex gravitational systems.