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dc.contributor.author
Colombo, Leonardo Jesus
dc.contributor.author
Ferraro, Sebastián José
dc.contributor.author
Martin de Diego, David
dc.date.available
2018-06-15T13:28:21Z
dc.date.issued
2016-12-01
dc.identifier.citation
Colombo, Leonardo Jesus; Ferraro, Sebastián José; Martin de Diego, David; Geometric Integrators for Higher-Order Variational Systems and Their Application to Optimal Control; Springer; Journal Of Nonlinear Science; 26; 6; 1-12-2016; 1615-1650
dc.identifier.issn
0938-8974
dc.identifier.uri
http://hdl.handle.net/11336/48751
dc.description.abstract
Numerical methods that preserve geometric invariants of the system, such as energy, momentum or the symplectic form, are called geometric integrators. In this paper we present a method to construct symplectic-momentum integrators for higher-order Lagrangian systems. Given a regular higher-order Lagrangian L: T( k )Q→ R with k≥ 1 , the resulting discrete equations define a generally implicit numerical integrator algorithm on T( k - 1 )Q× T( k - 1 )Q that approximates the flow of the higher-order Euler–Lagrange equations for L. The algorithm equations are called higher-order discrete Euler–Lagrange equations and constitute a variational integrator for higher-order mechanical systems. The general idea for those variational integrators is to directly discretize Hamilton’s principle rather than the equations of motion in a way that preserves the invariants of the original system, notably the symplectic form and, via a discrete version of Noether’s theorem, the momentum map. We construct an exact discrete Lagrangian Lde using the locally unique solution of the higher-order Euler–Lagrange equations for L with boundary conditions. By taking the discrete Lagrangian as an approximation of Lde, we obtain variational integrators for higher-order mechanical systems. We apply our techniques to optimal control problems since, given a cost function, the optimal control problem is understood as a second-order variational problem.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Springer
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.subject
Discrete Variational Calculus
dc.subject
Higher-Order Mechanics
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Optimal Control
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Variational Integrators
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Matemática Pura
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Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
Geometric Integrators for Higher-Order Variational Systems and Their Application to Optimal Control
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2018-06-07T16:12:44Z
dc.identifier.eissn
1432-1467
dc.journal.volume
26
dc.journal.number
6
dc.journal.pagination
1615-1650
dc.journal.pais
Alemania
dc.journal.ciudad
Berlín
dc.description.fil
Fil: Colombo, Leonardo Jesus. University of Michigan; Estados Unidos
dc.description.fil
Fil: Ferraro, Sebastián José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
dc.description.fil
Fil: Martin de Diego, David. Instituto de Ciencias Matemáticas; España. Consejo Superior de Investigaciones Científicas; España
dc.journal.title
Journal Of Nonlinear Science
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1007/s00332-016-9314-9
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00332-016-9314-9
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1410.5766
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