Normal Forms and Periodic Solutions in the Theory of Nonlinear Oscillations. Existence and Asymptotic Theory

摘要

A concept of normal forms is presented to analyze a class of O.D.E.'s arising from the field of nonlinear oscillations. An algorithm for the calculation of the normalized differential equations is presented as well as theorems on the existence, uniqueness and stability of periodic solutions and their calculation in an approximative way by using the normalized differential equations. As an application of the theory a simple model is discussed describing the flow-induced vibrations of an oscillator with one degree of freedom in an uniform windfield. The necessary calculations to perform the analysis have been done by an implementation of the algorithms for the calculation of higher order normal forms, as presented here, on the Computer-Algebra system Macsyma. (Copyright (c) 1988 by Faculty of Technical Mathematics and Informatics, Delft, The Netherlands.)