{"paper":{"title":"Magic mass ratios of complete energy-momentum transfer in one-dimensional elastic three-body collisions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.class-ph","authors_text":"June-Haak Ee, Jungil Lee","submitted_at":"2013-10-19T03:52:48Z","abstract_excerpt":"We consider the one-dimensional scattering of two identical blocks of mass $M$ that exchange energy and momentum via elastic collisions with an intermediary ball of mass $m=\\alpha M$. Initially, one block is incident upon the ball with the other block at rest. For $\\alpha<1$, the three objects will make multiple collisions with one another. In our analysis, we construct a Euclidean vector $\\textbf{V}_n$ whose components are proportional to the velocities of the objects. Energy-momentum conservation then requires a covariant recurrence relation for $\\textbf{V}_n$ that transforms like a pure rot"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5200","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"}