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

#### V.A. Malyshev

2018, v.24, Issue 2, 297-336

ABSTRACT

All physical laws are only approximation to reality in some range

of parameters. However, this does not mean that rigorous mathematics

is contraindicated 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.

Keywords: classical mechanics, point particles, introduction, Newton, Lagrange, Hamilton, Euler, BBGKY

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