On the problem of stability for higher-order derivative Lagrangian systems
type: Item
instance of: scholarly article
title: On the problem of stability for higher-order derivative Lagrangian systems
zbMATH Open document ID: 0656.70029
DOI: 10.1007/BF00402140
author: Giampietro Tecchiolli
author: Sergio Zerbini
author: Enrico Pagani
published in: Letters in Mathematical Physics
publication date: 1987-01-01T00:00:00Z
review text: The problem of stability for dynamical systems whose Lagrangian function depends on the derivatives of a higher order than one is studied. The difficulty of this analysis arises from the indefiniteness of the Hamiltonian, so that the well-known Lagrange-Dirichlet theorem cannot be used and the methods of the canonical perturbation theory (KAM theory) must be employed. We show, with an example, that the indefiniteness of the energy does not forbid the stability.
Mathematics Subject Classification ID: 70K20
Mathematics Subject Classification ID: 70H03
zbMATH DE Number: 4072485
zbMATH Keywords: stability
zbMATH Keywords: Lagrange-Dirichlet theorem
zbMATH Keywords: canonical perturbation theory
zbMATH Keywords: KAM theory
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00402140
OpenAlex ID: W2042340147
description: scientific article; zbMATH DE number 4072485