Un-Reduction of Systems of Second-Order Ordinary Differential Equations

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 te...

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Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2016
Hauptverfasser: García-Toraño Andrés, E., Mestdag, T.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут математики НАН України 2016
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/148551
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:Un-Reduction of Systems of Second-Order Ordinary Differential Equations / E. García-Toraño Andrés, T. Mestdag // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 19 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Zusammenfassung: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.
ISSN:1815-0659