On asymptotic approximations of first integrals for a class of nonlinear oscillators

In this thesis a class of nonlinear oscillator equations is studied. Asymptotic approximations of first integrals for the nonlinear differential equations are constructed by using the recently developed perturbation method based on integrating vectors. The existence and the stability of time-periodic solutions can be determined from these asymptotic approximations of the first integrals. Also asymptotic approximations of the solutions of the oscillator equations can be derived from these asymptotic approximations of the first integrals. Not only autonomous oscillator equations but also nonautonomous equations can be treated. In this thesis it is shown that the presented perturbation method based on integrating vectors can be applied to weakly and strongly nonlinear oscillator equations, which are "close" to integrable equations (that is, are integrable in the unperturbed case). In combination with a phase-space analysis and a Poincareturn-map technique the presented perturbation method gives a good insight in the global behavior of the solutions of the oscillator equations. All nonlinear oscillator equations which are studied in this thesis are simple model-equations describing the galloping oscillations of iced overhead power transmission lines in a windfield.Information Technology and System