Lagrangian-Hamiltonian unified formalism for autonomous higher-order dynamical systems
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.
Keywords
Cite
@article{arxiv.1106.3261,
title = {Lagrangian-Hamiltonian unified formalism for autonomous higher-order dynamical systems},
author = {Pedro D. Prieto-Martínez and Narciso Román-Roy},
journal= {arXiv preprint arXiv:1106.3261},
year = {2015}
}
Comments
36 pp. We have corrected and clarified the statement of Proposition 3. A remark is added after Proposition 3