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

V.A. Malyshev

2018, v.24, №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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