Displaying similar documents to “Natural Lagrangian structures”

Variational principles and symmetries on fibered multisymplectic manifolds

Jordi Gaset, Pedro D. Prieto-Martínez, Narciso Román-Roy (2016)

Communications in Mathematics

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The standard techniques of variational calculus are geometrically stated in the ambient of fiber bundles endowed with a (pre)multisymplectic structure. Then, for the corresponding variational equations, conserved quantities (or, what is equivalent, conservation laws), symmetries, Cartan (Noether) symmetries, gauge symmetries and different versions of Noether's theorem are studied in this ambient. In this way, this constitutes a general geometric framework for all these topics that includes,...

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

Ján Brajerčík (2011)

Czechoslovak Mathematical Journal

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Let μ : F X X be a principal bundle of frames with the structure group Gl n ( ) . It is shown that the variational problem, defined by Gl n ( ) -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.

The calculus of variations on jet bundles as a universal approach for a variational formulation of fundamental physical theories

Jana Musilová, Stanislav Hronek (2016)

Communications in Mathematics

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As widely accepted, justified by the historical developments of physics, the background for standard formulation of postulates of physical theories leading to equations of motion, or even the form of equations of motion themselves, come from empirical experience. Equations of motion are then a starting point for obtaining specific conservation laws, as, for example, the well-known conservation laws of momenta and mechanical energy in mechanics. On the other hand, there are numerous examples...

Generalized Jacobi morphisms in variational sequences

Francaviglia, Mauro, Palese, Marcella

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Summary: We provide a geometric interpretation of generalized Jacobi morphisms in the framework of finite order variational sequences. Jacobi morphisms arise classically as an outcome of an invariant decomposition of the second variation of a Lagrangian. Here they are characterized in the context of generalized Lagrangian symmetries in terms of variational Lie derivatives of generalized Euler-Lagrange morphisms. We introduce the variational vertical derivative and stress its link with...

Invariant variational problems on principal bundles and conservation laws

Ján Brajerčík (2011)

Archivum Mathematicum

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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.