Lagrangian-Hamiltonian unified formalism for autonomous higher order dynamical systems
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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.
CitationPrieto-Martínez, P.D.; Roman-Roy, N. Lagrangian-Hamiltonian unified formalism for autonomous higher order dynamical systems. "Journal of physics A. Mathematical and theoretical", 23 Setembre 2011, vol. 44, núm. 38, p. 1-36.