On the periodic solutions of a perturbed double pendulum
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 m...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2011 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:150406 |
| Acceso en línea: | https://ddd.uab.cat/record/150406 https://dx.doi.org/urn:doi:10.11606/issn.2316-9028.v5i2p317-330 |
| Access Level: | acceso abierto |
| Palabra clave: | Periodic solution Double pendulum Averaging theory |
| Sumario: | 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. |
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