Continuum Mechanics as Particle Mechanics

摘要

Here we want to understand what equations of continuum mechanics can be deduced directly (avoiding completely any randomness) from deterministic iV-particle mechanics as N →∞. Thus here our only axiom is Newton law. Another important axiom will be the conception of continuum media as consisting of the continuum number of particles of infinitely small mass. This conception is well known in mathematics, see for example [3], p. 56. We want to develop this rigorous conception and elaborate concrete examples, as many as possible.