{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,28]],"date-time":"2026-03-28T02:08:52Z","timestamp":1774663732728,"version":"3.50.1"},"reference-count":85,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,8,4]],"date-time":"2024-08-04T00:00:00Z","timestamp":1722729600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This study investigates the geometric linearization of constraint Hamiltonian systems using the Jacobi metric and the Eisenhart lift. We establish a connection between linearization and maximally symmetric spacetimes, focusing on the Noether symmetries admitted by the constraint Hamiltonian systems. Specifically, for systems derived from the singular Lagrangian LN,qk,q\u02d9k=12Ngijq\u02d9iq\u02d9j\u2212NV(qk), where N and qi are dependent variables and dimgij=n, the existence of nn+12 Noether symmetries is shown to be equivalent to the linearization of the equations of motion. The application of these results is demonstrated through various examples of special interest. This approach opens new directions in the study of differential equation linearization.<\/jats:p>","DOI":"10.3390\/sym16080988","type":"journal-article","created":{"date-parts":[[2024,8,5]],"date-time":"2024-08-05T18:21:40Z","timestamp":1722882100000},"page":"988","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Geometric Linearization for Constraint Hamiltonian Systems"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9966-5517","authenticated-orcid":false,"given":"Andronikos","family":"Paliathanasis","sequence":"first","affiliation":[{"name":"Institute of Systems Science, Durban University of Technology, P.O. Box 1334, Durban 4000, South Africa"},{"name":"School for Data Science and Computational Thinking, Stellenbosch University, 44 Banghoek Rd, Stellenbosch 7600, South Africa"},{"name":"Departamento de Matem\u00e1ticas, Universidad Cat\u00f3lica del Norte, Avda. Angamos 0610, Casilla, Antofagasta 1280, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,4]]},"reference":[{"key":"ref_1","unstructured":"Lie, S. (1970). Theorie der Transformationsgrupprn: Vol I, Chelsea."},{"key":"ref_2","unstructured":"Lie, S. (1970). Theorie der Transformationsgrupprn: Vol II, Chelsea."},{"key":"ref_3","unstructured":"Lie, S. (1970). Theorie der Transformationsgrupprn: Vol III, Chelsea."},{"key":"ref_4","unstructured":"Ibragimov, N.H. (2000). CRC Handbook of Lie Group Analysis of Differential Equations, Volume I: Symmetries, Exact Solutions, and Conservation Laws, CRS Press LLC."},{"key":"ref_5","unstructured":"Stephani, H. (1989). Differential Equations: Their Solutions Using Symmetry, Cambridge University Press."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Olver, P.J. (1993). 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