[Les solutions analytiques exactes pour le amortissable non linéaire oscillateur de Duffing]
Nous montrons que l'oscillateur de Duffing amorti peut être réduit à une équation équivalente à la forme normale d'équation d'Abel de seconde espèce. Sur la base d'une méthode développée récemment pour construction des solutions analytiques exactes de ce type d'équations d'Abel, des solutions analytiques exactes sont obtenues pour l'oscillateur de Duffing amorti, satisfaisant aux conditions initiales conformes au problème physique sousjacent. Pour illustrer la généralité de la méthode, une application à l'oscillateur de van der Pol est brièvement discutée.
We prove that the second-order damped nonlinear Duffing oscillator is reduced to an equivalent equation of the normal Abel form of the second kind. Based on a recently developed mathematical methodology for the construction of exact analytic solutions of Abel's equation, exact analytic solutions are obtained for the nonlinear damped Duffing oscillator obeying the initial conditions adapted to the physical problem. To improve the general developed methodology an application concerning the nonlinear Van der Pol free oscillator is briefly discussed.
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Publié le :
Mots-clés : Mécanique analytique, Non linéaire oscillateur de Duffing, Équation d'Abel
Dimitrios E. Panayotounakos 1 ; Efstathios E. Theotokoglou 1 ; Michalis P. Markakis 1
@article{CRMECA_2006__334_5_311_0,
author = {Dimitrios E. Panayotounakos and Efstathios E. Theotokoglou and Michalis P. Markakis},
title = {Exact analytic solutions for the damped {Duffing} nonlinear oscillator},
journal = {Comptes Rendus. M\'ecanique},
pages = {311--316},
publisher = {Elsevier},
volume = {334},
number = {5},
year = {2006},
doi = {10.1016/j.crme.2006.03.009},
language = {en},
}
TY - JOUR AU - Dimitrios E. Panayotounakos AU - Efstathios E. Theotokoglou AU - Michalis P. Markakis TI - Exact analytic solutions for the damped Duffing nonlinear oscillator JO - Comptes Rendus. Mécanique PY - 2006 SP - 311 EP - 316 VL - 334 IS - 5 PB - Elsevier DO - 10.1016/j.crme.2006.03.009 LA - en ID - CRMECA_2006__334_5_311_0 ER -
%0 Journal Article %A Dimitrios E. Panayotounakos %A Efstathios E. Theotokoglou %A Michalis P. Markakis %T Exact analytic solutions for the damped Duffing nonlinear oscillator %J Comptes Rendus. Mécanique %D 2006 %P 311-316 %V 334 %N 5 %I Elsevier %R 10.1016/j.crme.2006.03.009 %G en %F CRMECA_2006__334_5_311_0
Dimitrios E. Panayotounakos; Efstathios E. Theotokoglou; Michalis P. Markakis. Exact analytic solutions for the damped Duffing nonlinear oscillator. Comptes Rendus. Mécanique, Volume 334 (2006) no. 5, pp. 311-316. doi : 10.1016/j.crme.2006.03.009. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2006.03.009/
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