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A route to Routh—the parametric problem.

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Original title:A route to Routh—the parametric problem.
Author:Ladislav Adamec
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Original language:English
Field:General mathematics
Type:Article in Periodical
Keywords:Calculus of variations; Routh reduction; Poincare-Cartan form

There is a well known principle in classical mechanic stating that a variational problem independent of a space variable $w$ (so called cyclic variable), but dependent on the velocity $w'$ can be expressed without both $w$ and $w'$. This is the Routh reduction principle. We develop a geometrical approach to the problem and deal with general first order variational integrals admitting a Lie symmetry group of point transformations.

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