# Liouville's theorem and the foundation of classical mechanics

## TL;DR

This paper emphasizes the importance of Liouville's theorem as a foundational concept in classical mechanics, illustrating its role in deriving Hamiltonian dynamics and the principle of least action.

## Contribution

It presents Liouville's theorem as a pedagogical starting point for teaching classical mechanics and derives key principles from it.

## Key findings

- Liouville's theorem describes information conservation in classical mechanics.
- Hamilton equations are derived from Liouville's theorem.
- The Hamilton principle of least action is also derived from the theorem.

## Abstract

In this article, it is suggested that a pedagogical point of departure in the teaching of classical mechanics is the Liouville theorem. The theorem is interpreted to define the condition that describe the conservation of information in classical mechanics. The Hamilton equations and the Hamilton principle of least action are derived from the Liouville theorem.