Hilbert's 6-th Problem and Axiomatization of Dynamics

TL;DR

This paper proposes a new axiomatic framework for mechanics that generalizes Newton's second law to systems with variable mass, providing a more comprehensive understanding of dynamic behavior.

Contribution

It introduces an axiomatic basis of mechanics incorporating a principle of completeness to extend Newton's law for non-stationary variable-mass systems.

Findings

Hyperdynamic dependencies describe variable-mass motion more accurately

New qualitative insights into non-stationary systems

Generalization of classical mechanics principles

Abstract

The following offers a new axiomatic basis of mechanics and physics in their most important dynamics domain, i. e. an axiom (principle) of completeness intended to generalize Newton's second law of motion for the case of a non-stationary variable-mass point (system) that varies with time. This generalization leads to hyperdynamic dependencies describing such motion from new accurate qualitative standpoints.