2011/11/30 by Pedro D. Prieto-Martínez, Narciso Román-Roy
Physics and Astronomy · Mathematics · #math-ph #hep-th #math.MP #msc:70H50 #msc:53C80 #msc:37B55
paper · pdf · doi:10.1063/1.3692326
published as J. Math. Phys. 53(3) (2012) 032901 · 43 pp. We have corrected and clarified the statement of Propositions 2 and 3. A remark is added after Proposition 2
arxiv created 2012/10/23 · arxiv updated 2012/10/24
This work is devoted to giving a geometric framework for describing higher-order non-autonomous mechanical systems. The starting point is to extend the Lagrangian-Hamiltonian unified formalism of Skinner and Rusk for these kinds of systems, generalizing previous developments for higher-order autonomous mechanical systems and first-order non-autonomous mechanical systems. Then, we use this unified formulation to derive the standard Lagrangian and Hamiltonian formalisms, including the Legendre-Ostrogradsky map and the Euler-Lagrange and the Hamilton equations, both for regular and singular systems. As applications of our model, two examples of regular and singular physical systems are studied.