Czechoslovak Mathematical Journal, Vol. 61, No. 4, pp. 1063-1076, 2011

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:

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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