000121870 001__ 121870 000121870 005__ 20241125101128.0 000121870 0247_ $$2doi$$a10.3390/sym15010181 000121870 0248_ $$2sideral$$a132221 000121870 037__ $$aART-2023-132221 000121870 041__ $$aeng 000121870 100__ $$0(orcid)0000-0003-4480-6535$$aCariñena, José F.$$uUniversidad de Zaragoza 000121870 245__ $$aGeodesic and Newtonian vector fields and symmetries of mechanical systems 000121870 260__ $$c2023 000121870 5060_ $$aAccess copy available to the general public$$fUnrestricted 000121870 5203_ $$aGeodesic vector fields and other distinguished vector fields on a Riemann manifold were used in the study of free motions on such a manifold, and we applied the geometric Hamilton–Jacobi theory for the search of geodesic vector fields from Hamilton–Jacobi vector fields and the same for closed vector fields. These properties were appropriately extended to the framework of Newtonian and generalised Newtonian systems, in particular systems defined by Lagrangians of the mechanical type and velocity-dependent forces. Conserved quantities and a generalised concept of symmetry were developed, particularly for Killing vector fields. Nonholonomic constrained Newtonian systems were also analysed from this perspective, as well as the relation among Newtonian vector fields and Hamilton–Jacobi equations for conformally related metrics. 000121870 536__ $$9info:eu-repo/grantAgreement/ES/MICINN/PID2021-125515NB-C21$$9info:eu-repo/grantAgreement/ES/MICINN/PID2021-125515NB-C22$$9info:eu-repo/grantAgreement/ES/MICIU/PGC2018-098265-B-C31$$9info:eu-repo/grantAgreement/ES/MICIU/PGC2018-098265-B-C33 000121870 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000121870 590__ $$a2.2$$b2023 000121870 592__ $$a0.485$$b2023 000121870 591__ $$aMULTIDISCIPLINARY SCIENCES$$b50 / 134 = 0.373$$c2023$$dQ2$$eT2 000121870 593__ $$aChemistry (miscellaneous)$$c2023$$dQ2 000121870 593__ $$aPhysics and Astronomy (miscellaneous)$$c2023$$dQ2 000121870 593__ $$aMathematics (miscellaneous)$$c2023$$dQ2 000121870 593__ $$aComputer Science (miscellaneous)$$c2023$$dQ2 000121870 594__ $$a5.4$$b2023 000121870 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000121870 700__ $$aMuñoz-Lecanda, Miguel-C. 000121870 7102_ $$12004$$2405$$aUniversidad de Zaragoza$$bDpto. Física Teórica$$cÁrea Física Teórica 000121870 773__ $$g15, 1 (2023), 181 [39pp.]$$pSymmetry (Basel)$$tSymmetry$$x2073-8994 000121870 8564_ $$s510187$$uhttps://zaguan.unizar.es/record/121870/files/texto_completo.pdf$$yVersión publicada 000121870 8564_ $$s2417966$$uhttps://zaguan.unizar.es/record/121870/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000121870 909CO $$ooai:zaguan.unizar.es:121870$$particulos$$pdriver 000121870 951__ $$a2024-11-22-11:58:12 000121870 980__ $$aARTICLE