Variational and Optimal Control Approaches for the Second-Order Herglotz Problem on Spheres

Luís Machado (), Lígia Abrunheiro () and Natália Martins ()
Additional contact information
Luís Machado: University of Coimbra
Lígia Abrunheiro: University of Aveiro
Natália Martins: University of Aveiro

Journal of Optimization Theory and Applications, 2019, vol. 182, issue 3, No 6, 965-983

Abstract: Abstract The present paper extends the classical second-order variational problem of Herglotz type to the more general context of the Euclidean sphere $$S^n$$ S n following variational and optimal control approaches. The relation between the Hamiltonian equations and the generalized Euler–Lagrange equations is established. This problem covers some classical variational problems posed on the Riemannian manifold $$S^n$$ S n such as the problem of finding cubic polynomials on $$S^n$$ S n . It also finds applicability on the dynamics of the simple pendulum in a resistive medium.

Keywords: Variational problems of Herglotz type; Higher-order variational problems; Higher-order optimal control problems; Riemannian cubic polynomials; Euclidean sphere; 49K15; 49S05; 53B21; 34H05 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-018-1424-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:182:y:2019:i:3:d:10.1007_s10957-018-1424-0

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-018-1424-0

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().