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Once the dynamical equations are obtained, we conduct a parametric study based on the system\u2019s total energy and other key parameters such as the lengths and masses of the pendulums, as well as gravity, to determine the extent of the chaotic and regular regions in the phase space. Our numerical results reveal that, for a given mass ratio, the maximum chaotic fraction of phase space trajectories is attained when the pendulums have equal lengths. Furthermore, we characterize how chaos grows and decays within the system in terms of the model parameters, and explore the hypothesis that the chaotic fraction follows an exponential law over different energy regimes. <\/jats:p>","DOI":"10.1142\/s0218127424502018","type":"journal-article","created":{"date-parts":[[2024,11,29]],"date-time":"2024-11-29T10:23:38Z","timestamp":1732875818000},"source":"Crossref","is-referenced-by-count":5,"title":["Chaos and Regularity in the Double Pendulum with Lagrangian Descriptors"],"prefix":"10.1142","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-1498-246X","authenticated-orcid":false,"given":"Javier","family":"Jim\u00e9nez-L\u00f3pez","sequence":"first","affiliation":[{"name":"Departamento de F\u00edsica y Matem\u00e1ticas, Facultad de Ciencias, Universidad de Alcal\u00e1, 28805 Alcal\u00e1 de Henares, Madrid, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0557-3193","authenticated-orcid":false,"given":"V\u00edctor J.","family":"Garc\u00eda-Garrido","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica y Matem\u00e1ticas, Facultad de Ciencias, Universidad de Alcal\u00e1, 28805 Alcal\u00e1 de Henares, Madrid, Spain"}]}],"member":"219","published-online":{"date-parts":[[2024,11,28]]},"reference":[{"key":"S0218127424502018BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2004.11.092"},{"key":"S0218127424502018BIB004","doi-asserted-by":"publisher","DOI":"10.1051\/aas:2000108"},{"key":"S0218127424502018BIB005","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.65.2837"},{"key":"S0218127424502018BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2022.133520"},{"key":"S0218127424502018BIB007","doi-asserted-by":"publisher","DOI":"10.1063\/5.0064023"},{"key":"S0218127424502018BIB008","doi-asserted-by":"publisher","DOI":"10.1209\/0295-5075\/114\/40005"},{"key":"S0218127424502018BIB009","first-page":"203","volume":"3","author":"Deleanu D.","year":"2011","journal-title":"Ann. \u201cDunarea de Jos\u201d Univ. 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