Integration of near-resonant systems in slow-fluctuation approximation

DOI10.1063/1.524443zbMath0442.70028OpenAlexW1997195758MaRDI QIDQ3885271

Ernst Breitenberger, Marijke F. Augusteijn

Publication date: 1980

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

Full work available at URL: https://doi.org/10.1063/1.524443

zbMATH Keywords

perturbative effectsconservativetrigonometric polynomialautonomousnear-resonant systemsslow-fluctuation approximation

Mathematics Subject Classification ID

Hamilton's equations (70H05) Nonlinear resonances for nonlinear problems in mechanics (70K30)

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Root parities and phase behavior in the slow-fluctuation technique ⋮ Transient dynamics in strongly nonlinear systems: optimization of initial conditions on the resonant manifold ⋮ Waves, bifurcations, and solitons in a model with sixfold symmetry ⋮ Nonlinear targeted energy transfer: state of the art and new perspectives ⋮ On resonant classical Hamiltonians with n frequencies ⋮ [https://portal.mardi4nfdi.de/wiki/Publication:3028409 Analytische N�herungen und physikalische Deutung nichtlinearer Schwingungen mit inneren Resonanzen] ⋮ Bifurcation in a complex-valued wave-field model ⋮ The elastic pendulum: A nonlinear paradigm ⋮ Bifurcations in the slow-fluctuation technique ⋮ Stability of constant-amplitude motions in slow-fluctuation approximation

Cites Work

• [https://portal.mardi4nfdi.de/wiki/Publication:3264700 Stabilit�tsfragen bei freien Schwingungen mechanischer Systeme]
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• On resonance and stability of conservative systems
• An asymptotic solution to a problem involving two simultaneous small divisors
• Are higher order resonances really interesting?
• On a Class of Two-Degree-of-Freedom Oscillations
• A problem of orbital dynamics, which is separable in KS-variables
• Über die Resonanzschwingungen eines konservativen Systems
• Third and fourth order resonances in Hamiltonian systems
• Über den Zusammenhang zwischen Ausschlag und Schwingungsdauer bei der freien ungedämpften Schwingung

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