Smooth oscillating processes

Abstract

This chapter gives a brief overview of selected analytical methods for smooth oscillating processes. Most of such methods are indeed quasi-linear. In other words, the corresponding technical implementations employ harmonic oscillators as generating models. The description focuses only on the ideas and technical details that are further combined with non-smooth methods. As most effective way, procedures of asymptotic integration of the differential equations of motion bring original systems to such simple form that further solution becomes straightforward. In particular, the method of asymptotic integration of the differential equations of motion based on the Hausdorff equation for operators Lie is reproduced.