Lagrangian–Hamiltonian unified formalism for autonomous higher order dynamical systems

Abstract

The Lagrangian–Hamiltonian unified formalism of Skinner and 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 is 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.