Unified formalism for higher-order non-autonomous dynamical systems
Abstract
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.
Cite
@article{arxiv.1111.6020,
title = {Unified formalism for higher-order non-autonomous dynamical systems},
author = {Pedro D. Prieto-Martínez and Narciso Román-Roy},
journal= {arXiv preprint arXiv:1111.6020},
year = {2012}
}
Comments
43 pp. We have corrected and clarified the statement of Propositions 2 and 3. A remark is added after Proposition 2