Higher-order mechanics: Variational principles and other topics

Pedro D. Prieto-Martínez; Narciso Román-Roy

doi:10.3934/jgm.2013.5.493

Article Contents

2013, Volume 5, Issue 4: 493-510. Doi: 10.3934/jgm.2013.5.493

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Higher-order mechanics: Variational principles and other topics

Pedro D. Prieto-Martínez^1, and
Narciso Román-Roy^1,

1.
Departamento de Matemática Aplicada IV, Universitat Politècnica de Catalunya-BarcelonaTech, Campus Norte, Ed. C-3. C/ Jordi Girona 1, E-08034 Barcelona

Received: February 28, 2013

Revised: February 28, 2013

Published: November 2013

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Abstract

After reviewing the Lagrangian-Hamiltonian unified formalism (i.e, the Skinner-Rusk formalism) for higher-order (non-autonomous) dynamical systems, we state a unified geometrical version of the Variational Principles which allows us to derive the Lagrangian and Hamiltonian equations for these kinds of systems. Then, the standard Lagrangian and Hamiltonian formulations of these principles and the corresponding dynamical equations are recovered from this unified framework..

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Mathematics Subject Classification: Primary: 35A15, 37B55; Secondary: 70H50.

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