Capture and keeping of a resonance near equilibrium

DOI10.1134/S106192081902002XzbMath1467.34041OpenAlexW2948409980MaRDI QIDQ2424748

Leonid A. Kalyakin

Publication date: 25 June 2019

Published in: Russian Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s106192081902002x

zbMATH Keywords

nonlinear oscillationsaveraging methodssmall perturbationscapture into a resonance

Mathematics Subject Classification ID

Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Averaging method for ordinary differential equations (34C29) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Singular perturbations for ordinary differential equations (34E15) Asymptotic expansions of solutions to ordinary differential equations (34E05) Multifrequency systems of ordinary differential equations (34C46)

Cites Work

• Autoresonant asymptotics in an oscillating system with weak dissipation
• Finite-zone, almost-periodic solutions in WKB approximations
• Averaging for Hamiltonian systems with one fast phase and small amplitudes
• Asymptotic analysis of the model of gyromagnetic autoresonance
• Construction of an asymptotic solution of the auto-resonance problem. Inner decomposition
• Asymptotic solution of the threshold phenomenon problem for the principal resonance equations
• Capture into resonance and escape from it in a forced nonlinear pendulum
• Mathematical aspects of classical and celestial mechanics. Transl. from the Russian by E. Khukhro.
• Asymptotic behavior of solutions of equations of main resonance
• Asymptotic analysis of autoresonance models
• Averaging, passage through resonances, and capture into resonance in two-frequency systems
• Asymptotic solution to the problem of autoresonance: Outer expansion
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