Geodesic
Invariant variational problems on principal bundles and conservation laws
Archivum mathematicum, Tome 47 (2011) no. 5, pp. 357-366.

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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.
Classification : 49Q99, 49S05, 58A10, 58A20
Keywords: principal bundle; variational principle; invariant Lagrangian; Euler-Lagrange equations; Noether’s current; conservation law 
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     author = {Brajer\v{c}{\'\i}k, J\'an},
     title = {Invariant variational problems on principal bundles and conservation laws},
     journal = {Archivum mathematicum},
     pages = {357--366},
     publisher = {mathdoc},
     volume = {47},
     number = {5},
     year = {2011},
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     zbl = {1265.49049},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2011__47_5_a2/}
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Brajerčík, Ján. Invariant variational problems on principal bundles and conservation laws. Archivum mathematicum, Tome 47 (2011) no. 5, pp. 357-366. http://geodesic.mathdoc.fr/item/ARM_2011__47_5_a2/