# Hamiltonian & Lagrangian Mechanics

**Type:** Concept  
**Domain:** applied  
**Codex URL:** /mathematics/applied/hamiltonian-lagrangian-mechanics/  
**Entry status:** Live — v1.0 (2026-07-09)

## Summary
Energy-based reformulations of classical mechanics. Lagrange 1788: L=T-V, Euler-Lagrange equations. Hamilton 1833: H=T+V, Hamilton's equations, phase space, symplectic geometry, Poisson brackets. Canonical quantisation connects to quantum mechanics.

## Sources
- [Tier 1] Lagrange, J.-L. (1788). Mécanique analytique. Paris.
- [Tier 1] Arnold, V.I. (1989). Mathematical Methods of Classical Mechanics. 2nd ed. Springer.
- [Tier 2] Goldstein, H., Poole, C. and Safko, J. (2002). Classical Mechanics. 3rd ed.
- [Tier 3] Morin, D. (2008). Introduction to Classical Mechanics. Cambridge University Press.

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*Mathematics Codex entry v1.0 — added 2026-07-09 — thecodex.expert/mathematics/*