An introduction to the classical three-body problem: From periodic solutions to instabilities and chaos

TL;DR

This paper surveys the historical development of the classical three-body problem, highlighting its significance in understanding periodic solutions, instabilities, and chaos in classical mechanics.

Contribution

It provides a comprehensive overview of the three-body problem's history and introduces key ideas and techniques used to analyze complex mechanical systems.

Findings

Discovery of chaotic behavior in three-body systems

Development of methods for analyzing periodic solutions

Historical insights into the problem's significance

Abstract

The classical three-body problem arose in an attempt to understand the effect of the Sun on the Moon's Keplerian orbit around the Earth. It has attracted the attention of some of the best physicists and mathematicians and led to the discovery of chaos. We survey the three-body problem in its historical context and use it to introduce several ideas and techniques that have been developed to understand classical mechanical systems.