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Bibliographic Details
Main Authors: Przybylska, Maria, Maciejewski, Andrzej J.
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2504.17302
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author Przybylska, Maria
Maciejewski, Andrzej J.
author_facet Przybylska, Maria
Maciejewski, Andrzej J.
contents We consider the problem of $n$ points with positive masses interacting pairwise with forces inversely proportional to the distance between them. In particular, it is the classical gravitational, Coulomb or photo-gravitational $n$-body problem. Under this general form of interaction, we investigate the integrability problem of three bodies. We show that the system is not integrable except in one case when two among three interaction constants vanish. In our investigation, we used the Morales-Ramis theorem concerning the integrability of a natural Hamiltonian system with a homogeneous potential and its generalization.
format Preprint
id arxiv_https___arxiv_org_abs_2504_17302
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Non-integrability of charged three-body problem
Przybylska, Maria
Maciejewski, Andrzej J.
Chaotic Dynamics
We consider the problem of $n$ points with positive masses interacting pairwise with forces inversely proportional to the distance between them. In particular, it is the classical gravitational, Coulomb or photo-gravitational $n$-body problem. Under this general form of interaction, we investigate the integrability problem of three bodies. We show that the system is not integrable except in one case when two among three interaction constants vanish. In our investigation, we used the Morales-Ramis theorem concerning the integrability of a natural Hamiltonian system with a homogeneous potential and its generalization.
title Non-integrability of charged three-body problem
topic Chaotic Dynamics
url https://arxiv.org/abs/2504.17302