{"paper":{"title":"Linear stability of elliptic Lagrangian solutions of the planar three-body problem via index theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP","math.SG"],"primary_cat":"math.DS","authors_text":"Shanzhong Sun, Xijun Hu, Yiming Long","submitted_at":"2012-06-27T03:23:10Z","abstract_excerpt":"It is well known that the linear stability of Lagrangian elliptic equilateral triangle homographic solutions in the classical planar three-body problem depends on the mass parameter $\\bb=27(m_1m_2+m_2m_3+m_3m_1)/(m_1+m_2+m_3)^2\\in [0,9]$ and the eccentricity $e\\in [0,1)$. We are not aware of any existing analytical method which relates the linear stability of these solutions to the two parameters directly in the full rectangle $[0,9]\\times [0,1)$, besides perturbation methods for $e>0$ small enough, blow-up techniques for $e$ sufficiently close to 1, and numerical studies. In this paper, we in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.6162","kind":"arxiv","version":2},"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"}