{"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/structure-preserving-discretization-of-time","title":"Structure preserving discretization of time-reparametrized Hamiltonian systems with application to nonholonomic mechanics","arxiv_id":"2008.07222","date":"2020-08-17","proceeding":null,"authors":["Luis C. García-Naranjo","Mats Vermeeren"],"abstract":"We propose a discretization of vector fields that are Hamiltonian up to multiplication by a positive function on the phase space that may be interpreted as a time reparametrization. We prove that our method is structure preserving in the sense that the discrete flow is interpolated to arbitrary order by the flow of a continuous system possessing the same structure. In particular, our discretization preserves a smooth measure on the phase space to arbitrary order. We present applications to a remarkable class of nonholonomic mechanical systems that allow Hamiltonization. To our best knowledge, these results provide the first occurrence in the literature of a measure preserving discretization of measure preserving nonholonomic systems.","url_abs":"http://arxiv.org/abs/2008.07222v1","url_pdf":"http://arxiv.org/pdf/2008.07222v1.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":"structure-preserving-discretization-of-time","repo_url":"https://github.com/mvermeeren/conf-ham-sys-2020","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}