|
Эта публикация цитируется в 1 научной статье (всего в 1 статье)
Un-Reduction of Systems of Second-Order Ordinary Differential Equations
Eduardo García-Toraño Andrésa, Tom Mestdagb a Departamento de Matemática, Universidad Nacional del Sur, CONICET, Av. Alem 1253, 8000 Bahía Blanca, Argentina
b Department of Mathematics and Computer Science, University of Antwerp, Middelheimlaan 1, B-2020 Antwerpen, Belgium
Аннотация:
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.
Ключевые слова:
reduction; symmetry; principal connection; second-order ordinary differential equations; Lagrangian system.
Поступила: 12 августа 2016 г.; в окончательном варианте 29 ноября 2016 г.; опубликована 7 декабря 2016 г.
Образец цитирования:
Eduardo García-Toraño Andrés, Tom Mestdag, “Un-Reduction of Systems of Second-Order Ordinary Differential Equations”, SIGMA, 12 (2016), 115, 20 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma1197 https://www.mathnet.ru/rus/sigma/v12/p115
|
Статистика просмотров: |
Страница аннотации: | 110 | PDF полного текста: | 49 | Список литературы: | 20 |
|