{
  "id": "hamiltonian-lagrangian-mechanics",
  "domain": "applied",
  "type": "Concept",
  "title": "Hamiltonian & Lagrangian Mechanics",
  "slug": "hamiltonian-lagrangian-mechanics",
  "url": "/mathematics/applied/hamiltonian-lagrangian-mechanics/",
  "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.",
  "added_to_codex": "2026-07-09",
  "last_verified": "2026-07-09",
  "sources": [
    {
      "tier": 1,
      "citation": "Lagrange, J.-L. (1788). Mécanique analytique. Paris."
    },
    {
      "tier": 1,
      "citation": "Arnold, V.I. (1989). Mathematical Methods of Classical Mechanics. 2nd ed. Springer."
    },
    {
      "tier": 2,
      "citation": "Goldstein, H., Poole, C. and Safko, J. (2002). Classical Mechanics. 3rd ed."
    },
    {
      "tier": 3,
      "citation": "Morin, D. (2008). Introduction to Classical Mechanics. Cambridge University Press."
    }
  ],
  "entry_status": "live",
  "reading_levels_available": [
    "curious",
    "exploring",
    "deep_dive"
  ],
  "completeness": 1.0,
  "codex_version": "2.5"
}