{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/the-objective-deformation-component-of-a","title":"The Objective Deformation Component of a Velocity Field","arxiv_id":"2212.06617","date":"2022-12-13","proceeding":null,"authors":["Bálint Kaszás","Tiemo Pedergnana","George Haller"],"abstract":"For an arbitrary velocity field $\\mathbf{v}$ defined on a finite, fixed spatial domain, we find the closest rigid-body velocity field $\\mathbf{v}_{RB}$ to $\\mathbf{v}$ in the $L^2$ norm. The resulting deformation velocity component, $\\mathbf{v}_{d}=\\mathbf{v-\\mathbf{v}}_{RB}$, turns out to be frame-indifferent and physically observable. Specifically, if $\\mathbf{Q}_{\\text{RB}}(t)$ is the rotation tensor describing the motion of the closest rigid body frame, then $\\mathbf{v}$ is seen as $\\mathbf{Q}_{\\text{RB}}^{T}\\mathbf{v}_{d}$ by an observer in that frame. As a consequence, the momentum, energy, vorticity, enstrophy, and helicity of the flow all become frame-indifferent when computed from the deformation velocity component $\\mathbf{v}_{d}$.","url_abs":"https://arxiv.org/abs/2212.06617v1","url_pdf":"https://arxiv.org/pdf/2212.06617v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"the-objective-deformation-component-of-a","repo_url":"https://github.com/haller-group/deformationvelocity","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}