{"paper":{"title":"The vector field of a rolling rigid body","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS","math.MP","physics.class-ph"],"primary_cat":"math-ph","authors_text":"George W. Patrick","submitted_at":"2017-11-10T21:59:26Z","abstract_excerpt":"Nonholonomic systems are variational models commonly used for mechanical systems with ideal no-slip constraints. This note provides a differential-geometric derivation of the nonholonomic equations of motion for an arbitrary rigid body rolling on an arbitrary surface, via the semi-symplectic formalism, and in terms of shape operators (a.k.a. Weingarten maps). By a semi-symplectic reduction, the well-known differential equations in the case where the surface is a horizontal plane are shown to be semi-symplectic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.04028","kind":"arxiv","version":3},"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"}