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Pàgina inicial > Articles > Articles publicats > On the periodic solutions of a perturbed double pendulum |
Data: | 2011 |
Resum: | 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. |
Ajuts: | Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-410 |
Nota: | 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. |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Matèria: | Periodic solution ; Double pendulum ; Averaging theory |
Publicat a: | São Paulo Journal of Mathematical Sciences, Vol. 5 Núm. 2 (2011) , p. 317-330, ISSN 2316-9028 |
Postprint 11 p, 153.9 KB |