Abstract
The paper contains a brief survey of recent results obtained in the domain of non-linear mechanics by the pupils and successors of N.N. BOGOLUBOV, in the last decade. Of these results those concerning the development and mathematical justification of asymptotic methods with non-linear slowly-varying coefficients are treated in greater detail. The one-frequency method is described and justified. Problems of investigation of equations containing a small parameter are discussed on the basis of one- and two-dimensiona lintegral varieties.Also the typical problems of mechanical engineering, physics, theory of control etc. are mentioned. These problems have been treated by means of the methods of non-linear mechanics, thus enabling the development and generalization of these methods.
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