On Foundations of Newtonian Mechanics

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.