Inverse problem for Lagrangian systems on Lie algebroids and applications to reduction by symmetries

Barbero Liñán, María and Farré Puiggalí, Marta and Martín De Diego, David (2016). Inverse problem for Lagrangian systems on Lie algebroids and applications to reduction by symmetries. "Monatshefte für Mathematik", v. 180 (n. 4); pp. 665-691. ISSN 0026-9255. https://doi.org/10.1007/s00605-016-0893-1.

Description

Title: Inverse problem for Lagrangian systems on Lie algebroids and applications to reduction by symmetries
Author/s:
  • Barbero Liñán, María
  • Farré Puiggalí, Marta
  • Martín De Diego, David
Item Type: Article
Título de Revista/Publicación: Monatshefte für Mathematik
Date: August 2016
ISSN: 0026-9255
Volume: 180
Subjects:
Faculty: E.T.S. Arquitectura (UPM)
Department: Matemática Aplicada
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

The language of Lagrangian submanifolds is used to extend a geometric characterization of the inverse problem of the calculus of variations on tangent bundles to regular Lie algebroids. Since not all closed sections are locally exact on Lie algebroids, the Helmholtz conditions on Lie algebroids are necessary but not sufficient, so they give a weaker definition of the inverse problem. As an application the Helmholtz conditions on Atiyah algebroids are obtained so that the relationship between the inverse problem and the reduced inverse problem by symmetries can be described. Some examples and comparison with previous approaches in the literature are provided.

Funding Projects

TypeCodeAcronymLeaderTitle
Government of SpainSEV-2011-0087UnspecifiedUnspecifiedUnspecified
Government of SpainMTM2010-21186-C02-02UnspecifiedUnspecifiedEstructuras globales y métodos numéricos, sistemas dinámicos y control: aplicaciones cuánticas
FP7246981GEOMECHUnspecifiedGeometric Mechanics
Government of SpainMTM2010-21186-C02-01UnspecifiedUnspecifiedEstructuras globales y métodos numéricos, sistemas dinámicos y control cn aplicaciones en mecánica
Government of SpainMTM2013-42870-PUnspecifiedUnspecifiedEstructuras geométricas e integrabilidad en sistemas dinámicos y teoría de control

More information

Item ID: 48771
DC Identifier: http://oa.upm.es/48771/
OAI Identifier: oai:oa.upm.es:48771
DOI: 10.1007/s00605-016-0893-1
Official URL: https://link.springer.com/article/10.1007/s00605-016-0893-1
Deposited by: Memoria Investigacion
Deposited on: 18 Dec 2017 07:30
Last Modified: 03 Jun 2019 10:31
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