{"paper":{"title":"On the Geodesic Form of Non-Relativistic Dynamic Equations","license":"","headline":"","cross_cats":["math.DS","math.MP"],"primary_cat":"math-ph","authors_text":"G.Sardanashvily, L.Mangiarotti","submitted_at":"1999-06-01T06:31:14Z","abstract_excerpt":"It is shown that any second order dynamic equation on a configuration bundle $Q\\to R$ of non-relativistic mechanics is equivalent to a geodesic equation with respect to a (non-linear) connection on the tangent bundle $TQ\\to Q$. The case of quadratic dynamic equations is analyzed in details. The equation for Jacobi vector fields is constructed and investigated by the geometric methods."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/9906001","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"}