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Invariant variational problems on principal bundles and conservation laws

Ján Brajerčík — 2011

Archivum Mathematicum

In this work, we consider variational problems defined by G -invariant Lagrangians on the r -jet prolongation of a principal bundle P , where G is the structure group of P . These problems can be also considered as defined on the associated bundle of the r -th order connections. The correspondence between the Euler-Lagrange equations for these variational problems and conservation laws is discussed.

Order reduction of the Euler-Lagrange equations of higher order invariant variational problems on frame bundles

Ján Brajerčík — 2011

Czechoslovak Mathematical Journal

Let μ : F X → X be a principal bundle of frames with the structure group Gl n ( ℝ ) . It is shown that the variational problem, defined by Gl n ( ℝ ) -invariant Lagrangian on J r F X , can be equivalently studied on the associated space of connections with some compatibility condition, which gives us order reduction of the corresponding Euler-Lagrange equations.

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