The structure of the Euler-Lagrange mapping. (English) Zbl 1298.70023
Russ. Math. 51, No. 12, 52-70 (2007) and Izv. Vyssh. Uchebn. Zaved., Mat. 2007, No. 12, 51-69 (2007).
Summary: The purpose of this paper is to review properties of the Euler-Lagrange mapping in the higher order variational theory on fibred manifolds. We present basic theorems on the kernel of the Euler-Lagrange mapping, describing variationally trivial Lagrangians, and its image, characterizing variational source forms. We discuss invariance properties of Lagrangians and Euler-Lagrange forms, and the Noether’s theory.
MSC:
| 70G45 | Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics |
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