{"paper":{"title":"Euler-Poincar\\'e equations for $G$-Strands","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Darryl D. Holm, Rossen I. Ivanov","submitted_at":"2013-11-09T02:01:28Z","abstract_excerpt":"The $G$-strand equations for a map $\\mathbb{R}\\times \\mathbb{R}$ into a Lie group $G$ are associated to a $G$-invariant Lagrangian. The Lie group manifold is also the configuration space for the Lagrangian. The $G$-strand itself is the map $g(t,s): \\mathbb{R}\\times \\mathbb{R}\\to G$, where $t$ and $s$ are the independent variables of the $G$-strand equations. The Euler-Poincar\\'e reduction of the variational principle leads to a formulation where the dependent variables of the $G$-strand equations take values in the corresponding Lie algebra $\\mathfrak{g}$ and its co-algebra, $\\mathfrak{g}^*$ w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2126","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"}