Non-integrability of the n-body problem

2025/02/03 by Andrzej J. Maciejewski, Maciejewski, Andrzej J., Maria Przybylska +3 · 1 citation
Physics and Astronomy · Engineering · #Astro and Planetary Science #Spacecraft Dynamics and Control #Nuclear physics research studies

paper · pdf · doi:10.48550/arxiv.2502.01426

Abstract

We prove that the classical planar n-body problem when restricted to a common level of the energy and the angular momentum is not integrable except in the case when both values of these integrals are zero. In the proof of our theorem, we use methods of differential Galois theory.

Cited by

• Hamiltonian reduction from particular integrals

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