Un-reduction of systems of second-order ordinary differential equations

Eduardo García-Toraño Andrés and Tom Mestdag UGent (2016) 12.
abstract
In this paper we consider an alternative approach to "un-reduction". This is the process where one associates to a Lagrangian system on a manifold a dynamical system on a principal bundle over that manifold, in such a way that solutions project. We show that, when written in terms of second-order ordinary differential equations (SODEs), one may associate to the first system a (what we have called) "primary un-reduced SODE", and we explain how all other un-reduced SODEs relate to it. We give examples that show that the considered procedure exceeds the realm of Lagrangian systems and that relate our results to those in the literature.
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
reduction, symmetry, principal connection, second-order ordinary, differential equations, Lagrangian system
journal title
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS
Symmetry Integr. Geom.
volume
12
article number
115
pages
20 pages
Web of Science type
Article
Web of Science id
000389479600001
JCR category
PHYSICS, MATHEMATICAL
JCR impact factor
0.765 (2016)
JCR rank
45/55 (2016)
JCR quartile
4 (2016)
ISSN
1815-0659
DOI
10.3842/SIGMA.2016.115
language
English
UGent publication?
yes
classification
A1
I have retained and own the full copyright for this publication
id
8508885
handle
http://hdl.handle.net/1854/LU-8508885
alternative location
https://arxiv.org/abs/1606.07649
date created
2017-02-10 12:02:34
date last changed
2018-06-22 12:42:55
```@article{8508885,
abstract     = {In this paper we consider an alternative approach to {\textacutedbl}un-reduction{\textacutedbl}. This is the process where one associates to a Lagrangian system on a manifold a dynamical system on a principal bundle over that manifold, in such a way that solutions project. We show that, when written in terms of second-order ordinary differential equations (SODEs), one may associate to the first system a (what we have called) {\textacutedbl}primary un-reduced SODE{\textacutedbl}, and we explain how all other un-reduced SODEs relate to it. We give examples that show that the considered procedure exceeds the realm of Lagrangian systems and that relate our results to those in the literature.},
articleno    = {115},
author       = {Garc{\'i}a-Tora{\~n}o Andr{\'e}s, Eduardo and Mestdag, Tom},
issn         = {1815-0659},
journal      = {SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS},
keyword      = {reduction,symmetry,principal connection,second-order ordinary,differential equations,Lagrangian system},
language     = {eng},
pages        = {20},
title        = {Un-reduction of systems of second-order ordinary differential equations},
url          = {http://dx.doi.org/10.3842/SIGMA.2016.115},
volume       = {12},
year         = {2016},
}

```
Chicago
García-Toraño Andrés, Eduardo, and Tom Mestdag. 2016. “Un-reduction of Systems of Second-order Ordinary Differential Equations.” Symmetry Integrability and Geometry-methods and Applications 12.
APA
García-Toraño Andrés, E., & Mestdag, T. (2016). Un-reduction of systems of second-order ordinary differential equations. SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 12.
Vancouver
1.
García-Toraño Andrés E, Mestdag T. Un-reduction of systems of second-order ordinary differential equations. SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS. 2016;12.
MLA
García-Toraño Andrés, Eduardo, and Tom Mestdag. “Un-reduction of Systems of Second-order Ordinary Differential Equations.” SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS 12 (2016): n. pag. Print.