2011/06/30 by Pedro D. Prieto-Martínez, Narciso Román-Roy
Physics and Astronomy · Mathematics · #math-ph #hep-th #math.MP #msc:70H50 #msc:53C80 #msc:53C15
paper · pdf · doi:10.1088/1751-8113/44/38/385203
published as J. Phys A: Math. Theor. 44(38) (2011) 385203 (35pp) · 36 pp. We have corrected and clarified the statement of Proposition 3. A remark is added after Proposition 3
arxiv created 2012/10/23 · arxiv updated 2015/12/15
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.