{"paper":{"title":"Approximate action-angle variables for the figure-eight and other periodic three-body orbits","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","physics.class-ph"],"primary_cat":"math-ph","authors_text":"Milovan Suvakov, V. Dmitrasinovic","submitted_at":"2011-06-17T08:34:18Z","abstract_excerpt":"We use the maximally permutation symmetric set of three-body coordinates, that consist of the \"hyper-radius\" $R = \\sqrt{\\rho^{2} + \\lambda^{2}}$, the \"rescaled area of the triangle\" $\\frac{\\sqrt 3}{2 R^2} |{\\bm \\rho} \\times {\\bm \\lambda}|$) and the (braiding) hyper-angle $\\phi = \\arctan(\\frac{2{\\bm \\rho} \\cdot {\\bm \\lambda}}{\\lambda^2 - \\rho^2})$, to analyze the \"figure-eight\" choreographic three-body motion discovered by Moore \\cite{Moore1993} in the Newtonian three-body problem. Here ${\\bm \\rho}, {\\bm \\lambda}$ are the two Jacobi relative coordinate vectors. We show that the periodicity of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3413","kind":"arxiv","version":1},"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"}