A Huygens-Leibniz-Lange framework for classical mechanics

TL;DR

This paper proposes an alternative framework for classical mechanics based on ideas from Huygens, Leibniz, and Lange, addressing ambiguities in Newton's laws and rederiving standard results.

Contribution

It introduces a new set of laws for classical mechanics inspired by historical figures, avoiding Newton's ambiguities and applicable to relativistic particles.

Findings

Reproduces all standard results of classical mechanics

Addresses ambiguities in Newton's formulation

Extends to relativistic point particles

Abstract

I discuss the physical basis of classical mechanics, such as expressed commonly using the framework of Newton's Principia. Newton's formulation of the laws of motion is seen to have quite a few ambiguities and shortcomings. Therefore I offer an alternative set of laws, based in particular on ideas of his contemporaries Huygens and Leibniz with a crucial addition by Ludwig Lange, which avoids the problems with Newton's formulation. It is shown that from these laws of motion all the usual results of classical mechanics, as it concerns the motion of idealized point masses, can be rederived. The application of these principles to relativistic point particles is discussed.