Introduction

Abstract

This chapter contains physical and mathematical preliminaries with different introductory remarks. Although some of the statements are informal and rather intuitive, they nevertheless provide hints on selecting the generating models and corresponding analytical techniques. The idea is that simplicity of a mathematical formalism is caused by hidden links between the corresponding generating models and subgroups of rigid-body motions. Such motions may be qualified indeed as elementary macro-dynamic phenomena developed in the physical space. For instance, since rigid-body rotations are associated with sine waves and therefore (smooth) harmonic analyses then translations and mirror-wise reflections must reveal adequate tools for strongly unharmonic and nonsmooth approaches. This viewpoint is illustrated by physical examples, problem formulations and solutions.