Castrillón López, MarcoMarsden, Jerrold E.2023-06-202023-06-202008Abraham, R., Marsden, J.E.: Foundations of Mechanics (Benjamin-Cummings Publ. Co, Updated 1985 version, 2nd edn. reprinted by Perseus Publishing (1978) Bao, D., Marsden, J.E.,Walton, R.: The Hamiltonian structure of general relativistic perfect fluids. Comm. Math. Phys. 99, 319–345 (1985) Castrillón López, M., Marsden, J.E.: Some remarks on Lagrangian and Poisson reduction for field theories. J. Geom. Phys. 48, 52–83 (2003) Castrillón López, M., Muñoz Masqué, J.: The geometry of the bundle of connections. Math. Z. 236(4), 797–811 (2001) Castrillón López, M., Ratiu, T.S.: Reduction in principal bundles: covariant Lagrange-Poincaré equations. Comm. Math. Phys. 236(2), 223–250 (2003) Castrillón López, M., Ratiu, T.S., Shkoller, S.: Reduction inprincipal fiber bundles: covariant Euler-Poincaré equations. Proc. Amer. Math. Soc. 128(7), 2155–2164 (2000) Castrillón López, M., García Pérez, P.L., Ratiu, T.S.: Euler-Poincaré reduction on principal bundles. Lett. Math. Phys. 58(2), 167–180 (2001) Cendra, H., Marsden, J.E., Pekarsky, S., Ratiu, T.S.: Variational principles for Lie-Poisson and Hamilton- Poincaré equations. Mosc. Math. J. 3(3), 833–867 (2003) Cendra, H., Marsden, J.E., Ratiu, T.S.: Lagrangian reduction by stages. Mem. Amer. Math. Soc. 722, 1–108 (2001) García, P.L.: The Poincaré–Cartan invariant in the calculus of variation. In: Symposia Mathematica, Vol. XIV (Convegno di Geometria Simplettica e Fisica Matematica, INDAM, Rome, 1973), 53 #10037, 219–246 (Academic Press, London 1974) Gotay,M., Isenberg, J., Marsden, J.E.,Montgomery, R.:MomentumMaps and the Hamiltonian Structure of Classical Relativistic Field Theories I, Available at http://www.cds.caltech.edu/marsden/ (1997) Kobayashi, S., Nomizu, K.: Foundations of Differential Geometry, Wiley (1963) Marsden, J.E.,Misiołek, G., Ortega, J.-P., Perlmutter,M., Ratiu, T.S.: Hamiltonian Reduction by Stages, Springer Lecture Notes in Mathematics, vol. 1913. Springer-Verlag (2007) Marsden, J.E., Ratiu, T.S.: Introduction to Mechanics and Symmetry, volume 17 of Texts in Applied Mathematics, vol. 17; 1994, 2nd edn. Springer-Verlag (1999)0232-704X10.1007/s10455-008-9108-xhttps://hdl.handle.net/20.500.14352/50728Reduction for field theories with symmetry can be done either covariantly—that is, on spacetime—or dynamically—that is, after spacetime is split into space and time. The purpose of this article is to show that these two reduction procedures are, in an appropriate sense, equivalent for a class of field theories whose fields take values in a principal bundle. One can think of this class of field theories as including examples such as a “sea of rigid bodies” with and appropriate interbody coupling potential.engjournal articlehttp://link.springer.com/content/pdf/10.1007%2Fs10455-008-9108-x.pdfhttp://link.springer.com/restricted access515.16Variational calculus · Symmetries · Reduction · Euler–Poincare equationsGeometria algebraica1201.01 Geometría Algebraica