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Lagrangian-Hamiltonian unified formalism for field theory
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The RuskSkinner formalism was developed in order to give a geometrical unified formalism for describing mechanical systems. It incorporates all the characteristics of Lagrangian and Hamiltonian descriptions of these systems (including dynamical equations and solutions, constraints, Legendre map, evolution operators, equivalence, etc.). In this work we extend this unified framework to first-order classical field theories, and show how this description comprises the main features of the Lagrangian and Hamiltonian formalisms, both for the regular and singular cases. This formulation is a first step toward further applications in optimal control theory for partial differential equations. 2004 American Institute of Physics.
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ECHEVERRÍA ENRÍQUEZ, Arturo, et al. Lagrangian-Hamiltonian unified formalism for field theory. Journal of Mathematical Physics. 2004. Vol. 45, num. 1, pags. 360-380. ISSN 0022-2488. [consulted: 28 of June of 2026]. Available at: https://hdl.handle.net/2445/24583