000151184 001__ 151184 000151184 005__ 20251017144612.0 000151184 0247_ $$2doi$$a10.3390/sym13081413 000151184 0248_ $$2sideral$$a125869 000151184 037__ $$aART-2021-125869 000151184 041__ $$aeng 000151184 100__ $$0(orcid)0000-0003-4480-6535$$aCariñena J.F.$$uUniversidad de Zaragoza 000151184 245__ $$aJacobi multipliers in integrability and the inverse problem of mechanics 000151184 260__ $$c2021 000151184 5060_ $$aAccess copy available to the general public$$fUnrestricted 000151184 5203_ $$aWe review the general theory of the Jacobi last multipliers in geometric terms and then apply the theory to different problems in integrability and the inverse problem for one-dimensional mechanical systems. Within this unified framework, we derive the explicit form of a Lagrangian obtained by several authors for a given dynamical system in terms of known constants of the motion via a Jacobi multiplier for both autonomous and nonautonomous systems, and some examples are used to illustrate the general theory. Finally, some geometric results on Jacobi multipliers and their use in the study of Hojman symmetry are given. 000151184 536__ $$9info:eu-repo/grantAgreement/ES/MICIU/PGC2018-098265-B-C31 000151184 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttps://creativecommons.org/licenses/by/4.0/deed.es 000151184 590__ $$a2.94$$b2021 000151184 591__ $$aMULTIDISCIPLINARY SCIENCES$$b34 / 74 = 0.459$$c2021$$dQ2$$eT2 000151184 592__ $$a0.54$$b2021 000151184 593__ $$aChemistry (miscellaneous)$$c2021$$dQ2 000151184 593__ $$aPhysics and Astronomy (miscellaneous)$$c2021$$dQ2 000151184 593__ $$aComputer Science (miscellaneous)$$c2021$$dQ2 000151184 594__ $$a4.3$$b2021 000151184 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000151184 700__ $$aFernández-Núñez J. 000151184 7102_ $$12004$$2405$$aUniversidad de Zaragoza$$bDpto. Física Teórica$$cÁrea Física Teórica 000151184 773__ $$g13, 8 (2021), 1413 [30 pp.]$$pSymmetry (Basel)$$tSymmetry$$x2073-8994 000151184 8564_ $$s432865$$uhttps://zaguan.unizar.es/record/151184/files/texto_completo.pdf$$yVersión publicada 000151184 8564_ $$s2347764$$uhttps://zaguan.unizar.es/record/151184/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000151184 909CO $$ooai:zaguan.unizar.es:151184$$particulos$$pdriver 000151184 951__ $$a2025-10-17-14:17:53 000151184 980__ $$aARTICLE