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@article{931524, author = {Adamec, Ladislav}, article_number = {1}, doi = {http://dx.doi.org/10.1142/S1402925111001180}, keywords = {Calculus of variations; Routh reduction; Poincaré-Cartan form}, language = {eng}, issn = {1402-9251}, journal = {Journal of Nonlinear Mathematical Physic}, title = {A routhe to Routh -- the classical setting}, volume = {18}, year = {2011} }
TY - JOUR ID - 931524 AU - Adamec, Ladislav PY - 2011 TI - A routhe to Routh -- the classical setting JF - Journal of Nonlinear Mathematical Physic VL - 18 IS - 1 SP - 87-107 EP - 87-107 SN - 14029251 KW - Calculus of variations KW - Routh reduction KW - Poincaré-Cartan form N2 - 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. ER -
ADAMEC, Ladislav. A routhe to Routh -- the classical setting. \textit{Journal of Nonlinear Mathematical Physic}. 2011, vol.~18, No~1, p.~87-107. ISSN~1402-9251. Available from: https://dx.doi.org/10.1142/S1402925111001180.
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