equation 22.18 eq:ham-generating

Rests on

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Supports

• depends_on lemma 22.20 The symplectic condition ¶
  • depends_on corollary 22.24 Invariance of the phase-space volume ¶
    • depends_on remark 22.25 This is Liouville's theorem ¶
  • depends_on proposition 22.27 Properties of the Lagrange bracket ¶
    • depends_on remark 22.28 Where the content of the fundamental brackets lies ¶
  • depends_on proposition 22.30 Properties of the Poisson bracket ¶
    • depends_on remark 22.31 The bracket is a Lie algebra structure ¶
      • depends_on remark 22.39 Poisson's theorem does not manufacture new constants ¶
  • depends_on remark 22.33 What the duality is good for ¶
  • depends_on remark 22.28 Where the content of the fundamental brackets lies ¶ ↺
  • depends_on theorem 22.22 Poincaré ¶
    • depends_on proposition 32.40 A Hamiltonian section preserves area ¶
    • depends_on remark 22.23 What the invariant does not depend on ¶
• depends_on proposition 32.49 The small-denominator obstruction ¶
  • depends_on definition 32.50 Diophantine frequency vector ¶
    • depends_on theorem 32.51 Kolmogorov–Arnold–Moser, quoted ¶
      • depends_on phenomenon 32.58 Regular and chaotic motion coexist ¶
      • depends_on phenomenon 32.59 The solar system is chaotic ¶
      • depends_on remark 23.33 Integrability is exceptional ¶
• depends_on proposition 22.18 The mixed generating functions ¶
  • depends_on definition 23.2 Hamilton's principal function and the Hamilton–Jacobi equation ¶
    • depends_on remark 23.12 Two functions, two roles ¶
  • depends_on proposition A.556 The Jacobian of the actions is the lattice matrix ¶
    • depends_on example A.557 The check that fixes the convention ¶
  • depends_on remark 22.19 Which form exists ¶
  • depends_on theorem 23.30 Motion in action–angle variables ¶
    • depends_on example 23.24 Harmonic oscillator ¶
    • depends_on theorem 23.34 Adiabatic invariance of the action ¶
      • depends_on example 23.35 The slowly stiffened oscillator ¶
      • depends_on example 23.27 Charged particle in a uniform magnetic field ¶
      • depends_on remark 23.36 How good the invariance really is ¶
      • depends_on remark 23.37 Why this matters observationally ¶
    • depends_on theorem 23.31 Liouville–Arnold ¶
      • depends_on proposition 24.56 The Bohr–Sommerfeld condition is a triviality condition on the prequantum holonomy ¶
        • depends_on remark 24.57 The half-integer, and the honest status of the construction ¶
      • depends_on remark 23.33 Integrability is exceptional ¶ ↺
      • depends_on remark 23.32 What that proof imports ¶
      • depends_on theorem 32.51 Kolmogorov–Arnold–Moser, quoted ¶ ↺
      • depends_on theorem 32.47 Poincaré's non-integrability, quoted ¶