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Integral of motion in higher order mechanics and in field theory. (Czech) Zbl 0531.58021
The authors first give a survey of the modern geometrical methods used in the variational calculus on an arbitrary fibred manifold \(Y\to X\). Then they deduce a necessary and sufficient condition for Euler-like equations to be invariant with respect to a Lie transformation group G and variational, i.e. derived from and r-th order Lagrangian. As an example they discuss the case \(r=1\), \(Y={\mathbb{R}}\times {\mathbb{R}}^ 3\times {\mathbb{R}}^ 3\), \(X={\mathbb{R}}\) and \(G=\) the Galilean group.
Reviewer: I.Kolář
MSC:
58E30 Variational principles in infinite-dimensional spaces
49S05 Variational principles of physics
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