On Foundations of Newtonian Mechanics

TL;DR

This paper develops a unified theoretical framework connecting continuum mechanics and classical mechanics, deriving fundamental motion equations for various mechanical systems based on an axiomatic approach.

Contribution

It extends V. Konoplev's axiomatic approach to derive a comprehensive set of motion equations for different mechanical systems.

Findings

Derived Newton-Euler equations for point masses and multibody systems.

Formulated Lagrange equations of the second kind for complex systems.

Established Navier-Stokes equations within the axiomatic framework.

Abstract

Being based on V. Konoplev's axiomatic approach to continuum mechanics, the paper broadens its frontiers in order to bring together continuum mechanics with classical mechanics in a new theory of mechanical systems. There are derived motion equations of `abstract' mechanical systems specified for mass-points, multibody systems and continua: Newton-Euler equations, Lagrange equations of II kind and Navier-Stokes ones. Quasi-linear constitutive equations are introduced in conformity with V. Konoplev's definition of stress and strain (rate) matrices.