Lagrangian-Hamiltonian unified formalism for autonomous higher-order dynamical systems

Details Lagrangian-Hamiltonian unified formalism for autonomous higher-order dynamical systems Lagrangian-Hamiltonian unified formalism for autonomous higher-order dynamical systems

2011-06-16

arxiv.org/abs/1106.3261v3

J. Phys A: Math. Theor. 44(38) (2011) 385203 (35pp)

Physics

Mathematical Physics

Final version. Minor corrections. References added. 36 pp

Scientific paper

10.1088/1751-8113/44/38/385203

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.

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