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Title: Variational and optimal control approaches for the second-order Herglotz problem on spheres
Author: Machado, Luís
Abrunheiro, Lígia
Martins, Natália
Keywords: Variational problems of Herglotz type
Higher–order variational calculus
Higher–order optimal control problems
Riemannian cubic polynomials
Euclidean sphere.
Issue Date: 2018
Publisher: Springer
Abstract: The present paper extends the classical second–order variational problem of Herglotz type to the more general context of the Euclidean sphere Sn 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 Sn such as the problem of finding cubic polynomials on S^n. It also finds applicability on the dynamics of the simple pendulum in a resistive medium.
Peer review: yes
DOI: 10.1007/s10957-018-1424-0
ISSN: 0022-3239
Appears in Collections:CIDMA - Artigos
SCG - Artigos

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