Non-integrability of flail triple pendulum

TL;DR

This paper proves that a specific gravity-free triple pendulum system is non-integrable by analyzing its differential Galois group, combining numerical and analytical methods.

Contribution

It provides the first analytic proof of non-integrability for this particular triple pendulum configuration.

Findings

Poincaré sections indicate non-integrability.

Analytic proof based on differential Galois theory confirms non-integrability.

System remains non-integrable even without gravity.

Abstract

We consider a special type of triple pendulum with two pendula attached to end mass of another one. Although we consider this system in the absence of the gravity, a quick analysis of of Poincar\'e cross sections shows that it is not integrable. We give an analytic proof of this fact analysing properties the of differential Galois group of variational equation along certain particular solutions of the system.