On Huygens' derivation of the laws of elastic collisions

TL;DR

This paper explores Christiaan Huygens' historical derivation of elastic collision laws, emphasizing his use of relative motion and the conservation of living force, which influenced Leibniz's dynamics.

Contribution

It highlights Huygens' innovative approach to deriving elastic collision laws using relative motion and the conservation of living force, predating Newton's principles.

Findings

Huygens used relativity of uniform motion to derive conservation laws.

The conservation of living force was foundational in early dynamics.

Huygens' work influenced Leibniz's principles of motion.

Abstract

In this note I sketch the work of Christiaan Huygens to develop a theory of motion and its application to elastic collisions. In this theory he uses the relativity of uniform linear motion to derive the conservation of momentum and kinetic energy (at the time referred to as living force or vis viva). The conservation of living force was used subsequently by Leibniz as a basic general principle of dynamics, an alternative to that of Newton set forth in the Principia Mathematica.