{"paper":{"title":"An intrinsic formulation of the rolling manifolds problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Erlend Grong, F\\'atima Silva Leite, Irina Markina, Mauricio Godoy Molina","submitted_at":"2010-08-11T08:36:00Z","abstract_excerpt":"We present an intrinsic formulation of the kinematic problem of two $n-$dimensional manifolds rolling one on another without twisting or slipping. We determine the configuration space of the system, which is an $\\frac{n(n+3)}2-$dimensional manifold. The conditions of no-twisting and no-slipping are decoded by means of a distribution of rank $n$. We compare the intrinsic point of view versus the extrinsic one. We also show that the kinematic system of rolling the $n$-dimensional sphere over $\\mathbb R^n$ is controllable. In contrast with this, we show that in the case of $SE(3)$ rolling over $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1856","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"}