On the periodic solutions of a perturbed double pendulum
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Novaes, Douglas D. (Universidade Estadual de Campinas. Departamento de Matemática)
Teixeira, Marco Antonio (Universidade Estadual de Campinas. Departamento de Matemática)

Date:	2011
Abstract:	We provide sufficient conditions for the existence of periodic solutions of the planar perturbed double pendulum with small oscillations having equations of motion ¨θ1 = -2aθ1 + aθ2 + εF1(t, θ1, ˙θ1, θ2, ˙θ2), ¨θ2 = 2aθ1 - 2aθ2 + εF2(t, θ1, ˙θ1, θ2, ˙θ2), where a and ε are real parameters. The two masses of the unperturbed double pendulum are equal, and its two stems have the same length l. In fact a = g/l where g is the acceleration of the gravity. Here the parameter ε is small and the smooth functions F1 and F2 define the perturbation which are periodic functions in t and in resonance p:q with some of the periodic solutions of the unperturbed double pendulum, being p and q positive integers relatively prime.
Grants:	Ministerio de Ciencia e Innovación MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-410
Note:	Agraïments: The first and third authors are also supported by the joint project CA PES-MECD grant PHB-2009-0025-PC. The second author is partially suported by the grant FAPESP 2011/03896-0. The third author is partially supported by a FAPESP-BRAZIL grant 2007/06896-5.
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Document:	Article
Subject:	Periodic solution ; Double pendulum ; Averaging theory
Published in:	São Paulo Journal of Mathematical Sciences, Vol. 5 Núm. 2 (2011), p. 317-330, ISSN 2316-9028

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