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arXiv · 1106.3261

Lagrangian-Hamiltonian unified formalism for autonomous higher-order dynamical systems

Pedro D. Prieto-Martínez·Narciso Román-Roy
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Abstract

The Lagrangian-Hamiltonian unified formalism of R. Skinner and R. Rusk was originally stated for autonomous dynamical systems in classical mechanics. It has been generalized for non-autonomous first-order mechanical systems, as well as for first-order and higher-order field theories. However, a complete generalization to higher-order mechanical systems has yet to be described. In this work, after reviewing the natural geometrical setting and the Lagrangian and Hamiltonian formalisms for higher-order autonomous mechanical systems, we develop a complete generalization of the Lagrangian-Hamiltonian unified formalism for these kinds of systems, and we use it to analyze some physical models from this new point of view.

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Pedro D. Prieto-Martínez, Narciso Román-Roy. 2011-06-16. Lagrangian-Hamiltonian unified formalism for autonomous higher-order dynamical systems. https://doi.org/10.1088/1751-8113/44/38/385203

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