Geometric Hamiltonian Formulation of a Variational Problem Depending on the Covariant Acceleration | Zendy

Lígia Abrunheiro | Zendy; Margarida Camarinha | Zendy; Jesús Clemente-Gallardo | Zendy

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Geometric Hamiltonian Formulation of a Variational Problem Depending on the Covariant Acceleration

Author(s) -

Lígia Abrunheiro,

Margarida Camarinha,

Jesús Clemente-Gallardo

Publication year - 2013

Publication title -

conference papers in mathematics

Language(s) - English

Resource type - Journals

eISSN - 2314-4777

pISSN - 2314-5854

DOI - 10.1155/2013/243621

Subject(s) - covariant transformation , mathematics , tangent , acceleration , hamiltonian (control theory) , pontryagin's minimum principle , optimal control , context (archaeology) , calculus of variations , hamiltonian mechanics , variational integrator , mathematical analysis , classical mechanics , mathematical optimization , mathematical physics , geometry , computer science , physics , integrator , paleontology , phase space , biology , computer network , bandwidth (computing) , thermodynamics

In this work we consider a second order variational problem depending on the covariant acceleration, which is related with the notion of Riemannian cubic polynomials. This problem and the corresponding optimal control problem are described in the context of higher order tangent bundles using geometric tools. The main tool, a presymplectic variant of the Pontryagin's maximum principle, allows us to study the dynamics of the control problem

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