{"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/equations-of-motion-formulation-of-a-pendulum","title":"Equations of Motion Formulation of a Pendulum Containing N-point Masses","arxiv_id":"1910.12610","date":"2019-10-24","proceeding":null,"authors":["Boran Yesilyurt"],"abstract":"This paper presents a general formulation of equations of motion of a pendulum with n point mass by use of two different methods. The first one is obtained by using Lagrange Mechanics and mathematical induction(inspection), and the second one is derived by defining a vector. Today, these equations can be obtained by employing numerous programs; however, this study gives a very compact form of these equations that is more efficient than solving Euler-Lagrange Equations for every pendulum with more complex structures than simple or double pendulum. Additionally, we investigate what will happen to our n-point mass system when we take limit as number of point masses goes infinity under well-defined assumptions. We find out that it converges to hanging rope system.","url_abs":"https://arxiv.org/abs/1910.12610v2","url_pdf":"https://arxiv.org/pdf/1910.12610v2.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":"equations-of-motion-formulation-of-a-pendulum","repo_url":"https://github.com/lemonnuggets/n-pendulum","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"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}