Volume 21, Issue 4, October 2014, Pages 521 - 532
Integration of some examples of geodesic flows via solvable structures
Authors
Diego Catalano Ferraioli
Department of Mathematics, UFBA, Av Ademar de Barros s/n Salvador, BA CEP 40170-110, Brazildiego.catalano@ufba.br
Paola Morando
DISAA, Università degli Studi di Milano, Via Celoria, 2 Milano, 20133, Italypaola.morando@unimi.it
Received 17 March 2014, Accepted 16 June 2014, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2014.975525How to use a DOI?
- Keywords
- Solvable Structures; Variational Symmetries; Euler-Lagrange Equations
- Abstract
Solvable structures are particularly useful in the integration by quadratures of ordinary differential equations. Nevertheless, for a given equation, it is not always possible to compute a solvable structure. In practice, the simplest solvable structures are those adapted to an already known system of symmetries. In this paper we propose a method of integration which uses solvable structures suitably adapted to both symmetries and first integrals. In the variational case, due to Noether theorem, this method is particularly effective as illustrated by some examples of integration of the geodesic flows.
- Copyright
- © 2014 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 - Diego Catalano Ferraioli AU - Paola Morando PY - 2021 DA - 2021/01/06 TI - Integration of some examples of geodesic flows via solvable structures JO - Journal of Nonlinear Mathematical Physics SP - 521 EP - 532 VL - 21 IS - 4 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2014.975525 DO - 10.1080/14029251.2014.975525 ID - Ferraioli2021 ER -