{"paper":{"title":"Nonholonomic Noetherian symmetries and integrals of the Routh sphere and Chaplygin ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.SI"],"primary_cat":"nlin.CD","authors_text":"Miguel D. Bustamante, Peter Lynch","submitted_at":"2019-08-26T16:33:58Z","abstract_excerpt":"The dynamics of a spherical body with a non-uniform mass distribution rolling on a plane were discussed by Sergey Chaplygin, whose 150th anniversary we celebrate this year. The Chaplygin top is a non-integrable system, with a colourful range of interesting motions. A special case of this system was studied by Edward Routh, who showed that it is integrable.\n  The Routh sphere has centre of mass offset from the geometric centre, but it has an axis of symmetry through both these points, and equal moments of inertia about all axes orthogonal to the symmetry axis. There are three constants of motio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.09781","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.09781/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}