Ján Brajerčík, Department of Physics, Mathematics and Technology, University of Preąov, ul. 17. novembra 1, 081 16 Preąov, Slovak Republic, e-mail: email@example.com
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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