{"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/continuation-of-periodic-orbits-in","title":"Continuation of Periodic Orbits in Conservative Hybrid Dynamical Systems and its Application to Mechanical Systems with Impulsive Dynamics","arxiv_id":"2402.06502","date":"2024-02-09","proceeding":null,"authors":["Maximilian Raff","C. David Remy"],"abstract":"In autonomous differential equations where a single first integral is present, periodic orbits are well-known to belong to one-parameter families, parameterized by the first integral's values. This paper shows that this characteristic extends to a broader class of conservative hybrid dynamical systems (cHDSs). We study periodic orbits of a cHDS, introducing the concept of a hybrid first integral to characterize conservation in these systems. Additionally, our work presents a methodology that utilizes numerical continuation methods to generate these periodic orbits, building upon the concept of normal periodic orbits introduced by Sepulchre and MacKay (1997). We specifically compare state-based and time-based implementations of an cHDS as an important application detail in generating periodic orbits. Furthermore, we showcase the continuation process using exemplary conservative mechanical systems with impulsive dynamics.","url_abs":"https://arxiv.org/abs/2402.06502v4","url_pdf":"https://arxiv.org/pdf/2402.06502v4.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":"continuation-of-periodic-orbits-in","repo_url":"https://github.com/raffmax/conservativehybriddynamicalsystems","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}