equation 21.43 eq:lag-generalized-momentum

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• depends_on proposition 22.3 Invertibility of the Legendre map ¶
  • depends_on definition 26.3 Singular Lagrangian ¶
    • depends_on proposition 26.5 Primary constraints ¶
      • depends_on proposition 26.6 The canonical Hamiltonian is defined on the constraint surface ¶
        • depends_on definition 26.8 Total Hamiltonian ¶
      • depends_on proposition 26.32 Constraint structure of the free Maxwell field ¶
        • depends_on proposition 26.34 Proca constraints are second class ¶
        • depends_on proposition 26.37 Constraint structure of Yang–Mills theory ¶
      • depends_on proposition 26.29 Reparametrization invariance and the mass-shell constraint ¶
  • depends_on remark 22.4 When the Legendre map is singular ¶
• depends_on remark 22.5 Units ¶
  • depends_on remark 22.36 The whole dynamics in one operation ¶
  • depends_on remark 22.42 What the matrix form is for ¶
  • depends_on remark 24.11 The SI dimension of every object in this chapter ¶
    • depends_on remark 24.35 What non-squeezing does and does not say about nature ¶
    • depends_on remark 24.22 Liouville's theorem is the foundation of statistical mechanics ¶
    • depends_on remark 24.27 Fixing a scale, so that a ``ball'' means something ¶
      • depends_on definition 24.28 Ball and cylinder ¶
        • depends_on definition 24.33 Symplectic capacity ¶
        • depends_on example 24.29 A volume-preserving squeeze ¶
        • depends_on proposition 24.30 Linear non-squeezing ¶
        • depends_on theorem 24.31 Gromov's non-squeezing theorem ¶
      • depends_on definition 24.33 Symplectic capacity ¶ ↺
• depends_on theorem 22.6 Hamilton's equations ¶
  • 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 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 theorem 23.31 Liouville–Arnold ¶
    • depends_on remark 22.16 Why the class is larger than the point transformations ¶
  • 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 remark 23.8 The action as a function, not a functional ¶
• depends_on theorem 21.36 Conservation of the conjugate momentum ¶
  • depends_on proposition 23.14 Cyclic coordinates ¶
    • depends_on example 23.25 Central force in plane polar coordinates ¶ ↺
    • depends_on example 23.22 Free particle ¶ ↺
    • depends_on example 23.27 Charged particle in a uniform magnetic field ¶
    • depends_on example 23.23 Uniform gravity, and the parabola ¶ ↺
  • depends_on proposition 29.36 Three first integrals ¶
    • depends_on phenomenon 29.38 Nutation of a released top ¶
    • depends_on proposition 29.43 The three integrable heavy tops ¶
      • depends_on remark 29.45 What integrability buys, and where it stops ¶
      • depends_on remark 29.44 The Kovalevskaya integral ¶
    • depends_on proposition 29.40 The sleeping top ¶
    • depends_on theorem 29.37 Reduction to one degree of freedom ¶
      • depends_on phenomenon 29.38 Nutation of a released top ¶ ↺
      • depends_on proposition 29.40 The sleeping top ¶ ↺
      • depends_on remark 29.42 The closed form, and the mathematics it needs ¶