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

Symmetry Integrability and Geometry-Methods and Applications

article

Eduardo García-Toraño Andrés¹  Tom Mestdag² 

[1] Universidad Nacional del Sur;Department of Mathematics and Computer Science, University of Antwerp

关键词: reduction;    symmetry;    principal connection;    second-order ordinary dif ferential equations;    Lagrangian system;   

DOI  :  10.3842/SIGMA.2016.115

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown