The Herglotz variational problem on spheres and its optimal control approach

• Autor(a) principal: Abrunheiro, Lígia
• Data de Publicação: 2016
• Outros Autores: Machado, Luís, Martins, Natália
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10773/15635
• topic: Variational problems of Herglotz type; Calculus of variations; Optimal control problems; Geodesics on Riemannian manifolds; Euclidean sphere

The main goal of this paper is to extend the generalized variational problem of Herglotz type to the more general context of the Euclidean sphere S^n. Motivated by classical results on Euclidean spaces, we derive the generalized Euler-Lagrange equation for the corresponding variational problem defined on the Riemannian manifold S^n. Moreover, the problem is formulated from an optimal control point of view and it is proved that the Euler-Lagrange equation can be obtained from the Hamiltonian equations. It is also highlighted the geodesic problem on spheres as a particular case of the generalized Herglotz problem.