definition 21.31 Lagrangian

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• 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 22.2 Hamiltonian ¶
  • depends_on definition 22.14 Phase-space coordinate transformation ¶
    • depends_on definition 22.15 Canonical transformation ¶ ↺
    • depends_on definition 22.26 Lagrange bracket ¶
    • depends_on definition 22.29 Poisson bracket ¶
      • depends_on definition 26.20 Dirac bracket ¶
        • depends_on definition 26.23 Gauge conditions ¶
        • depends_on example 26.22 Holonomic constraints ¶
        • depends_on theorem A.617 Jacobi identity for the Dirac bracket ¶
        • depends_on theorem 26.21 Properties of the Dirac bracket ¶
      • depends_on definition 26.12 First and second class ¶
        • depends_on proposition 26.13 The first-class functions close ¶
        • depends_on proposition 26.19 Second-class constraints come in pairs ¶
        • depends_on proposition 26.34 Proca constraints are second class ¶
      • depends_on definition 26.8 Total Hamiltonian ¶
        • depends_on definition 26.16 Extended Hamiltonian ¶
        • depends_on theorem 26.21 Properties of the Dirac bracket ¶ ↺
        • depends_on theorem 26.14 First-class constraints generate gauge transformations ¶
      • depends_on definition 25.11 Generators of the Galilei transformations ¶
        • depends_on proposition 25.12 The algebra of generators closes ¶
      • depends_on definition 25.6 Infinitesimal canonical transformation ¶
        • depends_on definition 25.11 Generators of the Galilei transformations ¶ ↺
      • depends_on definition 25.2 Poisson algebra ¶
      • depends_on definition 24.36 Poisson manifold ¶
        • depends_on definition 25.2 Poisson algebra ¶ ↺
        • depends_on definition 24.37 Casimir function ¶
        • depends_on definition 24.40 Lie–Poisson bracket ¶
        • depends_on theorem 24.38 Symplectic foliation, quoted ¶
      • depends_on notation 26.28 Field systems ¶
        • depends_on definition 26.40 The $3+1$ decomposition ¶
        • depends_on notation A.636 Densities and smearing ¶
        • depends_on notation 26.36 Gauge fields and their SI dimensions ¶
      • depends_on notation 26.1 Weak and strong equality ¶
        • depends_on notation 26.28 Field systems ¶ ↺
      • depends_on proposition 24.15 Poisson bracket from the symplectic form ¶
        • depends_on definition 24.37 Casimir function ¶ ↺
        • depends_on theorem 24.45 Noether, symplectic form ¶
  • depends_on definition 23.15 Orthogonal Hamiltonian ¶
  • depends_on definition 25.18 Phase-space action ¶
  • depends_on theorem 22.6 Hamilton's equations ¶
    • depends_on definition 22.15 Canonical transformation ¶ ↺
    • depends_on remark 22.8 Non-conservative forces ¶
    • depends_on remark 22.7 Which half is kinematics and which is dynamics ¶
    • depends_on remark 23.4 What the equation costs and what it buys ¶
    • depends_on theorem 23.30 Motion in action–angle variables ¶ ↺
    • depends_on theorem 23.6 Jacobi ¶
      • depends_on example 23.25 Central force in plane polar coordinates ¶
      • depends_on example 23.22 Free particle ¶
        • depends_on remark 23.42 Phase speed and particle speed ¶
      • depends_on example 23.23 Uniform gravity, and the parabola ¶
      • depends_on proposition 23.7 The principal function is the action ¶ ↺
• depends_on definition 29.35 The Lagrange top ¶