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Czechoslovak Mathematical Journal, Vol. 61, No. 4, pp. 1063-1076, 2011
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#
Order reduction of the Euler-Lagrange equations

of higher order invariant variational

problems on frame bundles

##
Ján Brajerčík

* Ján Brajerčík*, Department of Physics, Mathematics and Technology, University of Preąov, ul. 17. novembra 1, 081 16 Preąov, Slovak Republic, e-mail: ` jan.brajercik@unipo.sk`

**Abstract:** Let $\mu FX \to X$ be a principal bundle of frames with the structure group $ Gl_n(\mathbb R)$. It is shown that the variational problem, defined by $ Gl_n(\mathbb R)$-invariant Lagrangian on $J^r FX$, 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.

**Keywords:** Frame bundle, Euler-Lagrange equations, invariant Lagrangian, Euler-Poincaré reduction

**Classification (MSC 2010):** 53C05, 53C10, 58A20, 58E30

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