Regularity properties of fiber derivatives associated with higher-order mechanical systems

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Title:	Regularity properties of fiber derivatives associated with higher-order mechanical systems
Author:	Colombo, Leonardo; Prieto Martínez, Pedro Daniel
Other authors:	Universitat Politècnica de Catalunya. DGDSA - Geometria Diferencial, Sistemes Dinàmics i Aplicacions
Abstract:	The aim of this work is to study fiber derivatives associated to Lagrangian and Hamiltonian functions describing the dynamics of a higher-order autonomous dynamical system. More precisely, given a function in T*T(k-1)Q, we find necessary and sufficient conditions for such a function to describe the dynamics of a kth-order autonomous dynamical system, thus being a kth-order Hamiltonian function. Then, we give a suitable definition of (hyper)regularity for these higher-order Hamiltonian functions in terms of their fiber derivative. In addition, we also study an alternative characterization of the dynamics in Lagrangian submanifolds in terms of the solutions of the higher-order Euler-Lagrange equations.
Abstract:	Peer Reviewed
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències -Classificació AMS::70 Mechanics of particles and systems::70H Hamiltonian and Lagrangian mechanics -Classificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry
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Document type:	Article - Published version Article
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