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The Journal of Geometric Mechanics (JGM)
 

Higher-order mechanics: Variational principles and other topics

Pages: 493 - 510, Volume 5, Issue 4, December 2013      doi:10.3934/jgm.2013.5.493

 
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Pedro D. Prieto-Martínez - Departamento de Matemática Aplicada IV, Universitat Politècnica de Catalunya-BarcelonaTech, Campus Norte, Ed. C-3. C/ Jordi Girona 1, E-08034 Barcelona, Spain (email)
Narciso Román-Roy - Departamento de Matemática Aplicada IV, Universitat Politècnica de Catalunya-BarcelonaTech, Campus Norte, Ed. C-3. C/ Jordi Girona 1, E-08034 Barcelona, Spain (email)

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..

Keywords:  Higher-order mechanics, Variational Principles, Lagrangian and Hamiltonian formalisms, Skinner-Rusk formulation, non-autonomous sytems.
Mathematics Subject Classification:  Primary: 35A15, 37B55; Secondary: 70H50.

Received: March 2013;      Revised: March 2013;      Available Online: December 2013.

 References