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Mathematical problems of nonlinearity

Estimation of the Accuracy of the Averaging Method for Systems with Multifrequency Perturbations

E. I. Kugushev, T. V. Popova

Lomonosov Moscow State University, GSP-1, Leninskie Gory, Moscow, 119991 Russia

Abstract: We consider systems of ordinary differential equations whose right-hand sides contain timeperiodic functions with some frequencies. An averaged system is constructed by introduction of additional variables and by step-by-step averaging over these variables. An upper estimate of the deviation of the solution to the initial system from the solution to the averaged system is given. Examples are given of mechanical systems in which vibrations with several frequencies occur and for the analysis of which the statements obtained are applied.

Keywords: averaging method, multifrequency perturbations, vibration frequency.

MSC: 34C29, 34C46

Received: 24.12.2019
Accepted: 15.03.2020

Language: English

DOI: 10.20537/nd200211

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