A routhe to Routh -- the classical setting

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Authors	ADAMEC Ladislav
Year of publication	2011
Type	Article in Periodical
Magazine / Source	Journal of Nonlinear Mathematical Physic
MU Faculty or unit	Faculty of Science
Citation
Doi	https://doi.org/10.1142/S1402925111001180
Field	General mathematics
Keywords	Calculus of variations; Routh reduction; Poincaré-Cartan form
Description	There is a well known principle in classical mechanic stating that a variational problem independent of a configuration space variable $w$ (so called cyclic variable), but dependent on its velocity $w'$ can be expressed without both $w$ and $w'$. This principle is known as the Routh reduction. In this paper we start to develop a purely geometric approach to this reduction. We do not limit ourselves to rather special problems of mechanics and in a certain sense we are able to obtain explicit formulae for the reduced variational integral.
Related projects:	Oscillatory and asymptotic properties of solutions of differential equations