Applications of the methods of averaging and successive approximations for studying nonlinear oscillations

DOI10.1016/0021-8928(81)90136-2zbMath0492.73020OpenAlexW2030079304MaRDI QIDQ1168102

L. D. Akulenko

Publication date: 1981

Published in: Journal of Applied Mathematics and Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8928(81)90136-2

zbMATH Keywords

existenceCauchy problemsufficient conditionssystem of ordinary differential equationssuccessive approximationsnonstationary processPicard methodsmoothness propertiesasymptotically large time intervalsstandard in sense of Bogoliubov

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Vibrations in dynamical problems in solid mechanics (74H45) Averaging method for ordinary differential equations (34C29) Nonlinear dynamics in mechanics (70K99) Numerical methods for initial value problems involving ordinary differential equations (65L05) Uniqueness of solutions of dynamical problems in solid mechanics (74H25) Uniqueness of solutions of equilibrium problems in solid mechanics (74G30)

Related Items (3)

Application of the method of two-scale expansions to the single-frequency problem of the theory of nonlinear oscillations ⋮ Averaging in a quasilinear system with a strongly varying frequency ⋮ Equivalent linearization of quasilinear oscillating systems with slowly varying parameters

Cites Work

• Approximate solution of nonlinear problems of optimal control of oscillatory processes using the method of canonical separation of motions
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