Gay-Balmaz, FrancoisRatiu, Tudor S.2011-12-162011-12-162011-12-16201010.5802/aif.2549https://infoscience.epfl.ch/handle/20.500.14299/75252WOS:000281235800011For symmetric classical field theories on principal bundles there are two methods of symmetry reduction: covariant and dynamic. Assume that the classical field theory is given by a symmetric covariant Lagrangian density defined on the first jet bundle of a principal bundle. It is shown that covariant and dynamic reduction lead to equivalent equations of motion. This is achieved by constructing a new Lagrangian defined on an infinite dimensional space which turns out to be gauge group invariant.Covariant reductiondynamic reductionaffine Euler-Poincare equationcovariant Euler-Poincare equationLagrangianprincipal bundle field theorytext::journal::journal article::research article