{"paper":{"title":"Isotropic submanifolds and the inverse problem for mechanical constrained systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SG"],"primary_cat":"math.DG","authors_text":"David Mart\\'in de Diego, Mar\\'ia Barbero-Li\\~n\\'an, Marta Farr\\'e Puiggal\\'i","submitted_at":"2014-04-07T22:15:41Z","abstract_excerpt":"The inverse problem of the calculus of variations consists in determining if the solutions of a given system of second order differential equations correspond with the solutions of the Euler-Lagrange equations for some regular Lagrangian. This problem in the general version remains unsolved. Here, we contribute to it with a novel description in terms of Lagrangian submanifolds of a symplectic manifold, also valid under some adaptation for the non-autonomous version. One of the advantages of this new point of view is that we can easily extend our description to the study of the inverse problem "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1961","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"}