remark 23.12 Two functions, two roles

Rests on

• depends_on definition 23.2 Hamilton's principal function and the Hamilton–Jacobi equation ¶
  • depends_on equation 22.21 eq:ham-F2 ¶
  • depends_on equation 23.1 eq:hj-K-zero ¶
  • depends_on proposition 22.18 The mixed generating functions ¶
    • depends_on definition 22.15 Canonical transformation ¶
      • depends_on definition 22.14 Phase-space coordinate transformation ¶
        • depends_on definition 22.2 Hamiltonian ¶
      • depends_on definition 21.45 Action ¶
        • depends_on definition 16.96 Action; Hamilton's principle ¶
        • depends_on equation 21.37 eq:lag-lagrangian ¶
      • depends_on theorem 22.6 Hamilton's equations ¶
        • depends_on definition 22.2 Hamiltonian ¶ ↺
        • depends_on equation 21.39 eq:lag-el-conservative ¶
        • depends_on equation 21.43 eq:lag-generalized-momentum ¶
        • proves proof ch:05-hamiltonian-mechanics@proof-2 ¶
    • depends_on equation 22.18 eq:ham-generating ¶
    • proves proof ch:05-hamiltonian-mechanics@proof-6 ¶
• depends_on proposition 23.9 Separation of the time ¶
  • depends_on equation 23.2 eq:hj-equation ¶
  • depends_on lemma 10.28 The separation constant ¶
    • depends_on definition 10.2 Linear, semilinear, quasilinear ¶
      • depends_on definition 10.1 Partial differential equation; order ¶
        • depends_on definition 7.98 Functions of class $C^{1}$ ¶
        • depends_on definition 6.2 Open set ¶
    • proves proof ch:08-pdes@proof-9 ¶
  • depends_on theorem 22.10 Conservation of the Hamiltonian ¶
    • depends_on proposition 22.9 Time derivative of the Hamiltonian ¶
      • depends_on equation 22.4 eq:ham-pdot ¶
      • depends_on equation 22.3 eq:ham-qdot ¶
      • proves proof ch:05-hamiltonian-mechanics@proof-3 ¶
    • proves proof ch:05-hamiltonian-mechanics@proof-4 ¶
  • proves proof ch:06-hamilton-jacobi@proof-3 ¶

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