Please use this identifier to cite or link to this item:
http://hdl.handle.net/10773/24659
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: | 2019 |
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 |
URI: | http://hdl.handle.net/10773/24659 |
DOI: | 10.1007/s10957-018-1424-0 |
ISSN: | 0022-3239 |
Appears in Collections: | CIDMA - Artigos SCG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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VARIATIONAL AND OPTIMAL CONTROL APPROACHES FOR THE SECOND–ORDER HERGLOTZ PROBLEM ON SPHERES - arxiv.pdf | 222.82 kB | Adobe PDF | View/Open |
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