Geodesic
Asymptotic Solution of the Autoresonance Problem
Teoretičeskaâ i matematičeskaâ fizika, Tome 133 (2002) no. 3, pp. 429-438

Voir la notice de l'article provenant de la source Math-Net.Ru

We study the problem of forced oscillations near a stable equilibrium of a two-dimensional nonlinear Hamiltonian system of equations. A given exciting force is represented as rapid oscillations with a small amplitude and a slowly varying frequency. We study the conditions under which such a perturbation makes the phase trajectory of the system recede from the original equilibrium point to a distance of the order of unity. To study the problem, we construct asymptotic solutions using a small amplitude parameter. We present the solution for not-too-small values of time outside the original boundary layer.
Keywords: nonlinear oscillations, resonance, asymptotic approximation, averaging. 
@article{TMF_2002_133_3_a8,
     author = {L. A. Kalyakin},
     title = {Asymptotic {Solution} of the {Autoresonance} {Problem}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {429--438},
     publisher = {mathdoc},
     volume = {133},
     number = {3},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2002_133_3_a8/}
}
TY  - JOUR
AU  - L. A. Kalyakin
TI  - Asymptotic Solution of the Autoresonance Problem
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2002
SP  - 429
EP  - 438
VL  - 133
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2002_133_3_a8/
LA  - ru
ID  - TMF_2002_133_3_a8
ER  - 
%0 Journal Article
%A L. A. Kalyakin
%T Asymptotic Solution of the Autoresonance Problem
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2002
%P 429-438
%V 133
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2002_133_3_a8/
%G ru
%F TMF_2002_133_3_a8
L. A. Kalyakin. Asymptotic Solution of the Autoresonance Problem. Teoretičeskaâ i matematičeskaâ fizika, Tome 133 (2002) no. 3, pp. 429-438. http://geodesic.mathdoc.fr/item/TMF_2002_133_3_a8/