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k-cosymplectic formalism in classical field theory: the Skinner–Rusk approach
(2006-02-14)
Article.
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Article.
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The k-cosymplectic Lagrangian and Hamiltonian formalisms of first-order field theories are
reviewed and completed. In particular they are stated for singular almost-regular systems. After that, both formalisms are unified ...
Some topics concerning the theory of singular dynamical systems
(2006-03-01)
Article.
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Article.
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Some subjects related to the geometric theory of singular dynamical systems are reviewed in this paper. In particular, the following two
matters are considered: the theory of canonical transformations for presymplectic ...
Geometric Hamilton–Jacobi Theory
(2006-04-21)
Article.
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Article.
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The Hamilton–Jacobi problem is revisited bearing in mind the consequences arising from a possible bi-Hamiltonian structure. The problem is formulated on the tangent bundle for Lagrangian systems in order to avoid the bias ...
Skinner-Rusk formalism for optimal control
(2006-12)
Article.
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Article.
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In 1983, the dynamics of a mechanical system was represented by a first-order system on a suitable phase space by R. Skinner and R. Rusk. The corresponding unified formalism developed for optimal control systems allows us ...
Multisymplectic Lagrangian and Hamiltonian formalisms of First-order Classical Field theories
(2006-03-03)
Article.
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Article.
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This review paper is devoted to presenting the standard multisymplectic formulation for
describing geometrically first-order classical field theories, both the regular and singular cases. First, the main features of the ...