Periodic solutions induced by an upright position of small oscillations of a sleeping symmetrical gyrostat
Guirao, Juan Luis Garcia (Universidad Politécnica de Cartagena. Departamento de Matemática Aplicada y Estadística)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Vera, Juan A. (Universidad Politécnica de Cartagena. Centro Universitario de la Defensa)

Date:	2013
Abstract:	The aim of this paper is to provide sufficient conditions for the existence of periodic solutions emerging from an upright position of small oscillations of a sleeping symmetrical gyrostat with equations of motion x¨ + αy˙ − βx = εF1 (t, x, x, y, ˙ y˙) , y¨ − αx˙ − βy = εF2 (t, x, x, y, ˙ y˙) being α and β parameters satisfying ∆ = α2 −4β > 0 and β −α2/2 ± α√∆/2 < 0, ε a small parameter and, F1 and F2 smooth periodic maps in the variable t in resonance p:q with some of the periodic solutions of the system for ε = 0, where p and q are positive integers relatively prime. The main tool used is the averaging theory.
Grants:	Ministerio de Ciencia y Tecnología MTM2011-22587 Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 European Commission 316338
Note:	Agraïments: The first author was partially supported by Junta de Comunidades de Castilla-La Mancha, grant number PEII09-0220-0222. The third author was partially supported by Fundación Séneca de la Región de Murcia grant number 12001/PI/09.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Periodic solution ; Symmetrical gyrostat ; Averaging theory
Published in:	Nonlinear Dynamics, Vol. 73 Núm. 1-2 (2013) , p. 417-425, ISSN 1573-269X

DOI: 10.1007/s11071-013-0797-8

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