A routhe to Routh -- the classical setting
| Authors | |
|---|---|
| Year of publication | 2011 |
| Type | Article in Periodical |
| Magazine / Source | Journal of Nonlinear Mathematical Physic |
| MU Faculty or unit | |
| Citation | |
| Doi | http://dx.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. |
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