Non-relativistic classical mechanics of point particles: shortest elementary introduction

摘要

All physical laws are only approximation to reality in some range of parameters. However, this does not mean that rigorous mathematics is con-traindicated to physics. On the contrary, inconsistencies and controversy of main physical laws give rise to dissatisfaction and urge inquiring minds to deeper plunging into the essence of things. Standard mathematical approach also should tend to the following ideal: 1) there should be axioms, the less the better. However, for some values of parameters they should be as close as possible to the basics of theoretical physics, 2) the range of corollaries and coordination with theoretical physics should be as wide as possible. We give a short mathematical introduction to the classical non-relativistic point particle physics. The goals are - to teach very beginner to do elementary calculations, to introduce him to most used terminology and to provide some global view on this science. Obviously this introduction is not suitable for deep concentration on some narrow part of particle mechanics. The necessary prerequisites - basics of the real analysis, linear algebra and ordinary differential equations.