Portal de Periódicos da CAPES

Lagrangian–Hamiltonian unified formalism for autonomous higher order dynamical systems

2011; Institute of Physics; Volume: 44; Issue: 38 Linguagem: Inglês

10.1088/1751-8113/44/38/385203

1751-8121

Pedro Daniel Prieto-Martínez, Narciso Román‐Roy,

Mechanical and Optical Resonators

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.