The asymptotic behavior of solutions to the repulsive $n$-body problem

TL;DR

This paper analyzes the long-term behavior of particles in a repulsive Coulomb $n$-body system, showing that particles move apart linearly over time with asymptotically straight trajectories and distinct velocities.

Contribution

It establishes the asymptotic linear growth of inter-particle distances and the straight-line trajectories with fixed velocities in the repulsive $n$-body problem.

Findings

Distances between particles grow linearly with time

Particles follow asymptotically straight trajectories

Each particle has a distinct asymptotic velocity

Abstract

The $n$-body problem with a purely repulsive Coulomb interaction is considered. It is shown that for large times $t$ the distance between any two particles grows linearly in $t$. The trajectory of each particle is asymptotically a straight line with a fixed velocity which is different for different particles.