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Constraints in Euler-Poincaré Reduction of Field Theories

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dc.contributor.authorCastrillón López, Marco
dc.date.accessioned2023-06-20T03:32:34Z
dc.date.available2023-06-20T03:32:34Z
dc.date.issued2012
dc.description.abstractThe goal of this short note is to show the geometric structure of the Euler-Poincaré reduction procedure in Field Theories with special emphasis on the nature of the set of variations and the set of admissible sections. The method of Lagrange multipliers is also applied for a deeper study of these constraints.
dc.description.departmentDepto. de Diseño e Imagen
dc.description.facultyFac. de Bellas Artes
dc.description.refereedTRUE
dc.description.sponsorshipICMAT (CSIC, UAM, UC3M, UCM),
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/21254
dc.identifier.doi10.1007/s10440-012-9695-1
dc.identifier.issn0167-8019
dc.identifier.officialurlhttp://link.springer.com/article/10.1007%2Fs10440-012-9695-1
dc.identifier.urihttps://hdl.handle.net/20.500.14352/43804
dc.issue.number1
dc.journal.titleActa Applicandae Mathematicae
dc.language.isoeng
dc.page.final99
dc.page.initial87
dc.publisherSpringer
dc.relation.projectIDMTM2010-19111;MTM2011-22528
dc.rights.accessRightsrestricted access
dc.subject.cdu514.745
dc.subject.keywordEuler-Poincaré equations Lagrange multipliers Reduction Symmetries Variational calculus
dc.subject.ucmGeometría diferencial
dc.subject.unesco1204.04 Geometría Diferencial
dc.titleConstraints in Euler-Poincaré Reduction of Field Theories
dc.typejournal article
dc.volume.number120
dcterms.referencesAbraham, R., Marsden, J.E.: Foundations of Mechanics. Benjamin/Cummings Publishing, Advanced Book Program, Reading (1978) Anderson, I.M., Fels, M.E., Torre, C.: Group invariant solutions without transversality and the principle of symmetric criticality. In: Bäcklund and Darboux transformations. The Geometry of Solitons, Halifax, NS, 1999. CRM Proc. Lecture Notes, vol. 29, pp. 95–108. Am. Math. Soc., Providence (2001) Arnold, V.I.: Mathematical Methods of Classical Mechanics, 2nd edn. Graduate Texts in Mathematics, vol. 60. Springer, New York (1989) Castrillón López, M., García, P.L., Ratiu, T.: Euler-Poincaré reduction on principal bundles. Lett. Math. Phys. 58(2), 167–180 (2001) Castrillón, M., García, P.L., Rodrigo, C.: Euler-Poincaré reduction in principal fibre bundles and the problem of Lagrange. Differ. Geom. Appl. 25(6), 585–593 (2007) Castrillón López, M.,Marsden, J.: Some remarks on Lagrangian and Poisson reduction for field theories. J. Geom. Phys. 48(1), 52–83 (2003) Castrillón López, M., Muñoz Masqué, J.: The geometry of the bundle of connections. Math. Z. 236(4), 797–811 (2001) García, P.L.: The Poincaré-Cartan invariant in the calculus of variations. Symp. Math. 14, 219–246 (1974) Giachetta, G., Mangiarotti, L., Sarnanashvily, G.: New Lagrangian and Hamiltonian Methods in Field Theory. World Scientific, Singapore (1997) Goldschmidt, H., Sternberg, S.: The Hamiltonian-Cartan formalism in the calculus of variations. Ann. Inst. Fourier 23(1), 203–267 (1973) Kobayashi, S., Numizu, K.: Foundations of Differential Geometry, vol. I. Wiley-Interscience, New York (1963) Kobayashi, S., Numizu, K.: Foundations of Differential Geometry, vol. II.Wiley-Interscience, New York (1969) Marsden, J.E., Patrick, G., Shkoller, S.: Multisymplectic geometry, variational integrators, and nonlinear PDEs. Commun. Math. Phys. 199, 351–395 (1998) Marsden, J.E., Ratiu, T.S.: Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems, 2nd edn. Texts in Applied Mathematics, vol. 17. Springer, New York (1999) Moser, J., Veselov, A.: Discrete versions of some classical integrable systems and factorization of matrix polynomials. Commun. Math. Phys. 139(2), 217–243 (1991) Saunders, D.J.: The Geometry of Jet Manifolds. Cambridge University Press, Cambridge (1989) Vankerschaver, J.: Euler-Poincaré reduction for discrete field theories. J. Math. Phys. 48(3) (2007)
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relation.isAuthorOfPublication32e59067-ef83-4ca6-8435-cd0721eb706b
relation.isAuthorOfPublication.latestForDiscovery32e59067-ef83-4ca6-8435-cd0721eb706b

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