{"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/all-about-the-galilean-group-sgal-3","title":"All About the Galilean Group SGal(3)","arxiv_id":"2312.07555","date":"2023-12-08","proceeding":null,"authors":["Jonathan Kelly"],"abstract":"We consider the Galilean group of transformations that preserve spatial distances and absolute time intervals between events in spacetime. The special Galilean group, SGal(3), is a 10-dimensional Lie group; we examine the structure of the group and its Lie algebra and discuss the representation of uncertainty on the group manifold. Along the way, we mention several other groups, including the special orthogonal group, the special Euclidean group, and the group of extended poses, all of which are proper subgroups of the Galilean group. We describe the role of time in Galilean relativity and touch on the relationship between temporal and spatial uncertainty.","url_abs":"https://arxiv.org/abs/2312.07555v10","url_pdf":"https://arxiv.org/pdf/2312.07555v10.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":"all-about-the-galilean-group-sgal-3","repo_url":"https://github.com/artivis/manif","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"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}