equation 16.11 eq:calcvar-basic-functional

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Supports

• depends_on definition 16.96 Action; Hamilton's principle ¶
  • depends_on definition 16.99 Abbreviated action ¶
    • depends_on definition 23.28 Action variables ¶
      • depends_on example 23.24 Harmonic oscillator ¶
      • depends_on proposition 23.38 Bohr–Sommerfeld and Einstein–Brillouin–Keller quantization ¶
        • depends_on remark 24.57 The half-integer, and the honest status of the construction ¶
      • 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 23.29 Convention ¶
      • depends_on remark 29.45 What integrability buys, and where it stops ¶
      • 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 theorem 23.31 Liouville–Arnold ¶
      • depends_on theorem 23.34 Adiabatic invariance of the action ¶ ↺
    • depends_on proposition 23.10 The characteristic function is the abbreviated action ¶
      • depends_on remark 23.11 Whose principle, and where it fails ¶
  • depends_on definition 21.45 Action ¶
    • depends_on definition 22.15 Canonical transformation ¶
      • depends_on proposition 22.17 Transformation conditions ¶
        • depends_on remark 22.21 The count ¶
      • 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 proposition A.556 The Jacobian of the actions is the lattice matrix ¶
        • depends_on remark 22.19 Which form exists ¶
        • depends_on theorem 23.30 Motion in action–angle variables ¶ ↺
      • depends_on remark 22.16 Why the class is larger than the point transformations ¶
  • depends_on definition 28.3 Simple harmonic oscillator ¶
  • depends_on proposition 23.7 The principal function is the action ¶
    • depends_on remark 23.8 The action as a function, not a functional ¶
• depends_on definition 16.83 One-parameter transformation group; variational symmetry ¶
• depends_on lemma 16.72 Convexity implies weak lower semicontinuity ¶
  • depends_on theorem A.448 Tonelli ¶
  • depends_on theorem A.456 Convexity in $q$ implies weak lower semicontinuity ¶
  • depends_on theorem 16.73 Tonelli ¶
• depends_on proposition 16.17 The first variation of an integral functional ¶
  • depends_on theorem 16.43 Euler's rule for integral constraints ¶
    • depends_on example 16.45 Two solved isoperimetric problems ¶
    • depends_on proposition 16.4 The hanging chain is a catenary ¶
    • depends_on proposition 16.6 The isoperimetric extremal is a circle ¶
  • depends_on theorem 16.84 Noether's first theorem, one independent variable ¶
    • depends_on theorem 16.90 Noether's first theorem, several independent variables ¶
      • depends_on theorem 16.93 Noether's second theorem ¶
        • depends_on example 16.109 The Einstein–Hilbert action ¶
        • depends_on theorem 44.19 Covariant conservation of stress–energy ¶
• depends_on theorem A.448 Tonelli ¶ ↺