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Title: | Energy-based theory of autoresonance phenomena: application to Duffing-like systems |
Other Titles: | General exact theory of autoresonance in nonautonomous systems |
Authors: | Chacón García, Ricardo |
Keywords: | Autorresonancia;Sistemas no autónomos;Sistema Hamiltoniano;Sistema Duffing;Autoresonance;Nonautonomous system;Hamiltonian system;Duffing-like system |
Issue Date: | 2006 |
Publisher: | EDP Sciences |
Source: | Chacón, Ricardo. Energy-based theory of autoresonance phenomena: application to Duffing-like systems. ArXiv: physics/0306139v3 |
Abstract: | Se presenta una teoría basada en la energía general de autorresonancia (resonancia autosostenida) en los sistemas no autónomos de baja dimensión. Las ecuaciones que deciden las soluciones y las excitaciones de autorresonancia se derivan con ayuda de un principio de variación relativa a la potencia funcional. La teoría es aplicada a los sistemas de Duffing para obtener expresiones analíticas exactas para excitaciones y soluciones de autorresonancia que explican todos los resultados fenomenológicos y aproximados a partir del enfoque anterior (adiabática), próximos a fenómenos de resonancia en tales sistemas. La teoría también se aplica para obtener nuevas, generales y exactas propiedades relativas a fenómenos de resonancia en una amplia clase de sistemas disipativos y hamiltonianos, incluyendo (como caso particular) el sistema de Duffing. A general energy-based theory of autoresonance (self-sustained resonance) in low-dimensional nonautonomous systems is presented. The equations that together govern the autoresonance solutions and excitations are derived with the aid of a variational principle concerning the power functional. These equations provide a feedback autoresonance-controlling mechanism. The theory is applied to Duffing-like systems to obtain exact analytical expressions for autoresonance excitations and solutions which explain all the phenomenological and approximate results arising from a previous (adiabatic) approach to aud resonance phenomena in such systems. The theory is also applied to obtain new, general, and exact properties concerning auto resonance phenomena in a broad class of dissipative and Hamiltonian systems, including (as a particular case) Duffing-like systems. |
Description: | Publicado en: Europhysics Letters, Vol. 70, No 1, pp. 56-62 (2005) |
URI: | http://hdl.handle.net/10662/21985 |
ISSN: | 0295-5075 |
DOI: | 10.1209/epl/i2004-10465-1 |
Appears in Collections: | DFIAP - Artículos |
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arxiv_physics_0306139.pdf | 270,14 kB | Adobe PDF | View/Open |
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