2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78980Let $π:P\to M^n$ be a principal G-bundle, and let ${\mathcal{L}}: J^1P \toΛ^n(M)$ be a G-invariant Lagrangian density. We obtain the Euler-Poincare equations for the reduced Lagrangian l defined on ${\mathcal C}(P)$, the bundle of connections on P.Differential GeometryMathematical Physics53C05; 53C10text