{"paper":{"title":"Morse index and linear stability of the Lagrangian circular orbit in a three-body-type problem via index theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alessandro Portaluri, Riccardo D. Jadanza, Vivina Barutello","submitted_at":"2014-06-13T12:37:00Z","abstract_excerpt":"It is well known that the linear stability of the Lagrangian elliptic solutions in the classical planar three-body problem depends on a mass parameter $\\beta$ and on the eccentricity $e$ of the orbit. We consider only the circular case ($e = 0$) but under the action of a broader family of singular potentials: $\\alpha$-homogeneous potentials, for $\\alpha \\in (0,2)$, and the logarithmic one. It turns out indeed that the Lagrangian circular orbit persists also in this more general setting. We discover a region of linear stability expressed in terms of the homogeneity parameter $\\alpha$ and the ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3519","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}