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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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