Relative non-relativistic mechanics

TL;DR

This paper reformulates non-relativistic mechanics using covariant coordinates based on relative velocities and accelerations, clarifying concepts like reference frames and inertial forces.

Contribution

It introduces a covariant-coordinate framework for non-relativistic mechanics, emphasizing relative quantities and providing a clearer conceptual foundation.

Findings

Reformulation of mechanics in covariant form

Clarification of inertial frames and forces

Unified description of free motion

Abstract

Dynamic equations of non-relativistic mechanics are written in covariant-coordinate form in terms of relative velocities and accelerations with respect to an arbitrary reference frame. The notions of the non-relativistic reference frame, inertial force, free motion equation, and inertial frame are discussed.