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A route to Routh—the parametric problem.

Basic information
Original title:A route to Routh—the parametric problem.
Author:Ladislav Adamec
Further information
Citation:ADAMEC, Ladislav. A route to Routh—the parametric problem. Acta Applicandae Mathematicae, Kluwer, 2012, vol. 117, No 1, p. 115–134. ISSN 0167-8019. doi:10.1007/s10440-011-9654-2.Export BibTeX
@article{985974,
author = {Adamec, Ladislav},
article_number = {1},
doi = {http://dx.doi.org/10.1007/s10440-011-9654-2},
keywords = {Calculus of variations; Routh reduction; Poincare-Cartan form},
language = {eng},
issn = {0167-8019},
journal = {Acta Applicandae Mathematicae},
title = {A route to Routh—the parametric problem.},
volume = {117},
year = {2012}
}
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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