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

Ján Brajerčík

Czechoslovak Mathematical Journal (2011)

  • Volume: 61, Issue: 4, page 1063-1076
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Brajerčík, Ján. "Order reduction of the Euler-Lagrange equations of higher order invariant variational problems on frame bundles." Czechoslovak Mathematical Journal 61.4 (2011): 1063-1076. <http://eudml.org/doc/196784>.

@article{Brajerčík2011,
abstract = {Let $\mu \colon FX \rightarrow X$ be a principal bundle of frames with the structure group $\{\rm Gl\}_\{n\}(\mathbb \{R\})$. It is shown that the variational problem, defined by $\{\rm Gl\}_\{n\}(\mathbb \{R\})$-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.},
author = {Brajerčík, Ján},
journal = {Czechoslovak Mathematical Journal},
keywords = {Frame bundle; Euler-Lagrange equations; invariant Lagrangian; Euler-Poincaré reduction; frame bundle; Euler-Lagrange equations; invariant Lagrangian; Euler-Poincaré reduction},
language = {eng},
number = {4},
pages = {1063-1076},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Order reduction of the Euler-Lagrange equations of higher order invariant variational problems on frame bundles},
url = {http://eudml.org/doc/196784},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Brajerčík, Ján
TI - Order reduction of the Euler-Lagrange equations of higher order invariant variational problems on frame bundles
JO - Czechoslovak Mathematical Journal
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 4
SP - 1063
EP - 1076
AB - Let $\mu \colon FX \rightarrow X$ be a principal bundle of frames with the structure group ${\rm Gl}_{n}(\mathbb {R})$. It is shown that the variational problem, defined by ${\rm Gl}_{n}(\mathbb {R})$-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.
LA - eng
KW - Frame bundle; Euler-Lagrange equations; invariant Lagrangian; Euler-Poincaré reduction; frame bundle; Euler-Lagrange equations; invariant Lagrangian; Euler-Poincaré reduction
UR - http://eudml.org/doc/196784
ER -

References

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