{"paper":{"title":"Mechanical Systems in the Generalized Lie Algebroids Framework","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.MP"],"primary_cat":"math-ph","authors_text":"Constantin M. Arcus","submitted_at":"2013-10-06T05:53:44Z","abstract_excerpt":"\\emph{Mechanical systems} called by use, \\emph{mechanical}$\\left(\\rho ,\\eta\\right) $\\emph{-systems, Lagrange mechanical}$\\left(\\rho ,\\eta \\right) $\\emph{-systems} or \\emph{Finsler mechanical}$\\left(\\rho ,\\eta \\right) $\\emph{-systems} are presented. The canonical $\\left(\\rho ,\\eta \\right) $\\emph{-}semi(spray) associated to a mechanical $\\left(\\rho ,\\eta \\right) $-system is obtained. New and important results are obtained in the particular case of Lie algebroids. The Lagrange mechanical $(\\rho ,\\eta)$% -systems are the spaces necessary to develop a new Lagrangian formalism. We obtain the $(\\rho "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2131","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"}