{"paper":{"title":"Rolling Manifolds of Different Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Amina Mortada, Petri Kokkonen, Yacine Chitour","submitted_at":"2013-12-17T18:16:20Z","abstract_excerpt":"If $(M,g)$ and $(\\hM,\\hg)$ are two smooth connected complete oriented Riemannian manifolds of dimensions $n$ and $\\hn$ respectively, we model the rolling of $(M,g)$ onto $(\\hM,\\hg)$ as a driftless control affine systems describing two possible constraints of motion: the first rolling motion $\\Sigma_{NS}$ captures the no-spinning condition only and the second rolling motion $\\Sigma_{R}$ corresponds to rolling without spinning nor slipping. Two distributions of dimensions $(n + \\hn)$ and $n$, respectively, are then associated to the rolling motions $\\Sigma_{NS}$ and $\\Sigma_{R}$ respectively. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4885","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"}