Non-integrability of the dumbbell and point mass problem

TL;DR

This paper proves that a gravitational three-body system with a dumbbell-shaped mass configuration is non-integrable, using differential Galois theory to establish the complexity of its dynamics.

Contribution

It introduces a novel three-body problem with a dumbbell configuration and demonstrates its non-integrability through advanced mathematical methods.

Findings

The system is proven to be non-integrable.

Differential Galois theory effectively analyzes complex gravitational systems.

The dumbbell configuration leads to chaotic dynamics.

Abstract

This paper discusses a constrained gravitational three-body problem with two of the point masses separated by a massless inflexible rod to form a dumbbell. The non-integrability of this system is proven using differential Galois theory.