Introduction

Lagrangian mechanics provided us with a powerful way to describe motion using energy. However, an even more general and elegant formulation exists — Hamiltonian mechanics.

This formulation is especially important because:

• It forms the foundation of quantum mechanics
• It introduces powerful concepts like phase space
• It provides deep insight into conservation laws and symmetries

Hamiltonian mechanics reformulates dynamics in terms of energy and momentum variables, rather than position and velocity.