{"paper":{"title":"Weakly nonlinear analysis of Hopf bifurcations in the elastohydrodynamics of Cosserat rods","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.soft","math.MP","physics.flu-dyn"],"primary_cat":"math-ph","authors_text":"Mohamed Warda","submitted_at":"2026-05-14T11:17:52Z","abstract_excerpt":"We study the weakly nonlinear saturation of the flutter instability of a planar Cosserat rod in a viscous fluid driven by a terminal follower force. This instability, established in our preceding work as a Hopf bifurcation of a non-self-adjoint linear operator, produces stable limit-cycle oscillations in the fully nonlinear overdamped dynamics. Here we derive an analytical description of the emergence of this limit cycle near threshold. Working close to the critical follower force, we perform a multiple-scale expansion about the compressed straight base state and systematically remove secular "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.14702","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"}