Non-integrability of the minimum-time Kepler problem

TL;DR

This paper proves that the minimum-time Kepler problem cannot be solved using integrable meromorphic functions, indicating fundamental limits on its solvability with classical integrability methods.

Contribution

It applies the Morales-Ramis theory to establish the non-integrability of the minimum-time Kepler problem in the meromorphic function class.

Findings

The minimum-time Kepler problem is not Liouville integrable in the meromorphic class.

The proof uses Morales-Ramis theory to demonstrate non-integrability.

This result highlights inherent complexity in solving the minimum-time Kepler problem.

Abstract

We prove that the minimum-time controlled Kepler problem is not Liouville integrable in the class of meromorphic functions, via the Moral\`es-Ramis theory.