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
Citation:
Kugushev E. I., Popova T. V., Estimation of the Accuracy of the Averaging Method for Systems with Multifrequency Perturbations, Rus. J. Nonlin. Dyn.,
2020, Vol. 16, no. 2,
pp. 379-394
DOI:10.20537/nd200211