{"paper":{"title":"Quadratic conservation laws and collineations: a discussion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.MP"],"primary_cat":"gr-qc","authors_text":"Andronikos Paliathanasis, Leonidas Karpathopoulos, Michael Tsamparlis","submitted_at":"2018-07-25T16:57:25Z","abstract_excerpt":"Every second order system of autonomous differential equations can be described by an autonomous holonomic dynamical system with a Lagrangian part, an effective potential and a set of generalized forces. The kinematic part of the Lagrangian defines the kinetic metric which subsequently defines a Riemannian geometry in the configuration space. We consider the generic function $I=K_{ab}(t,q^{c})\\dot{q}^{a}\\dot{q}^{b}+K_{a}(t,q^{c})\\dot{q}% ^{a}+K(t,q^{c})$ and require the quadratic first integral condition $dI/dt=0$ without involving any type of symmetry Lie or Noether. Condition $dI/dt=0$ leads"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.09721","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"}