On Concept of Mechanical System

TL;DR

This paper develops a screw axiomatics framework for rational mechanics, introducing new measures and principles to unify classical mechanical systems through advanced vector calculus concepts.

Contribution

It presents a novel axiomatic approach using screw measures and vector calculus to formalize the fundamental principles of rational mechanics.

Findings

Defines new measures of mechanics including screw measures of motion and action.

Establishes a local integral conservation law for the vector measure of motion.

Provides a unified framework for classical mechanical systems using screw measures.

Abstract

The paper gives a screw axiomatics of rational mechanics, namely: 1. introduces the main measures of mechanics: the mass measure, the scalar and (vector) screw measures of motion, the (vector) screw measure of impressed action, the increment velocity of the vector measure of motion, the (vector) screw measure of constraint action; 2. postulates the (stronger) local integral form of conservation law for the vector measuare of motion (fundamental principle of dynamics), and 3. defines the central concept of rational mechanics {mechanical system being realized in the form of all classical mechanical systems (mass-points, rigid bodies, continua, point-bodies, etc.). The presentation is based on new notions of vector calculus -- homogeneous and inhomogeneous vector and tensor slider-functions and screw measures.