A Route to Routh — The Classical Setting
- 10.1142/S1402925111001180How to use a DOI?
- Calculus of variations; Routh reduction; cyclic variables; Poincaré–Cartan form; Noether's theorem
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.
- © 2011 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Ladislav Adamec PY - 2021 DA - 2021/01/07 TI - A Route to Routh — The Classical Setting JO - Journal of Nonlinear Mathematical Physics SP - 87 EP - 107 VL - 18 IS - 1 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925111001180 DO - 10.1142/S1402925111001180 ID - Adamec2021 ER -