Application of first-order canonical perturbation method with dissipative Hori-like kernel

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Title: Application of first-order canonical perturbation method with dissipative Hori-like kernel
Authors: Baenas, Tomás | Escapa García, Luis Alberto | Ferrandiz, Jose M. | Getino, Juan
Research Group/s: Grupo de Fotoquímica y Electroquímica de Semiconductores (GFES) | Geodesia Espacial y Dinámica Espacial
Center, Department or Service: Universidad de Alicante. Departamento de Matemática Aplicada
Keywords: Perturbation theory | Non-canonical system | Non-linear system | Hamiltonian Mechanics
Knowledge Area: Matemática Aplicada
Issue Date: Apr-2017
Publisher: Elsevier
Citation: International Journal of Non-Linear Mechanics. 2017, 90: 11-20. doi:10.1016/j.ijnonlinmec.2016.12.017
Abstract: Lie-Hori canonical perturbation theory provides asymptotic solutions for conservative Hamiltonian systems. This restriction prevents the canonical method from being applied directly to dissipative mechanical systems. There are, however, two main alternatives to overcome this difficulty, enabling the application of canonical perturbation methods. The first one consists in constructing a time-dependent Hamiltonian, through a generating function, related to the energy dissipation pattern of the system. The second embeds the original phase space into a double dimensional one where the dynamics of the system can be formulated in a Hamiltonian way. In this paper, a modified Lie-Hori method that avoid the disadvantages of the former approaches is proposed. Namely, it is not necessary to find out a time-dependent generating function, nor doubling the number of the canonical variables of the original problem. The new algorithm provides first order analytical solutions for a certain set of dissipative non-linear dynamical systems. It is based on a suitable modification of the Hori kernel in the double-dimensional embedding phase space, allowing the inclusion of the dissipative (or generalized) forces. By means of this redefined auxiliary system, the path-integrals of the method can be performed in a domain of the phase space with the same dimensionality as the original problem.
Sponsor: This research has been partially supported by the Spanish government MINECO projects AYA2010-22039-C02-02 and AYA2016-79775-P (AEI/FEDER, UE).
ISSN: 0020-7462 (Print) | 1878-5638 (Online)
DOI: 10.1016/j.ijnonlinmec.2016.12.017
Language: eng
Type: info:eu-repo/semantics/article
Rights: © 2016 Elsevier Ltd.
Peer Review: si
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Appears in Collections:INV - GEDE - Artículos de Revistas
INV - GFES - Artículos de Revistas

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