Abstract
In this paper an asymptotic analytic solving method for a differential equation with complex function, small nonlinearity and a slow variable parameter is developed. The procedure is an extension of the well known Bogolubov-Mitropolski method. The correctness of the procedure is proved by an example. The vibrations of a rotor on which a thin band is wound and on which a small linear damping acts are obtained. The analytical solutions are compared with numerical ones. They are in good agreement.
Sommario
Nel presente lavoro viene sviluppato un metodo asintotico per la risoluzione analitica di equazioni differenziali di variabile complessa con piccola non-linearità e parametro lentamente variabile. La procedura proposta è un'estensione del ben noto metodo di Bogolubov-Mitropolski. La correttezza di tale procedura è provata su di un esempio. Sono ottenute le vibrazioni di un rotore su cui viene arrotolato uno strato sottile ed agisce un piccolo smorzamento lineare. Le soluzioni analitiche sono comparate con quelle numeriche con cui sono in buon accordo.
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Cveticanin, L. Approximate solution of a time-dependent differential equation. Meccanica 30, 665–671 (1995). https://doi.org/10.1007/BF00986572
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DOI: https://doi.org/10.1007/BF00986572