proposition 26.13 The first-class functions close

open in the book · parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:353 · p. 903

Rests on

depends_on definition 26.12 First and second class ¶
- depends_on definition 26.11 The final constraint set ¶
  - depends_on proposition 26.10 The four outcomes ¶
    - depends_on definition 26.9 Consistency conditions ¶
      - depends_on equation 26.7 eq:cd-evolution ¶
      - depends_on equation 26.2 eq:cd-primary ¶
    - depends_on remark 26.7 The regularity assumption, stated once ¶
    - proves proof ch:09-constrained-hamiltonian-dynamics@proof-3 ¶
  - depends_on remark 26.7 The regularity assumption, stated once ¶ ↺
- depends_on definition 22.29 Poisson bracket ¶
  - depends_on definition 7.97 Partial derivative; gradient ¶
    - depends_on definition 7.26 Derivative of a function at a point ¶
      - depends_on definition 7.16 Limit ¶
      - depends_on definition 7.9 Real function ¶
    - depends_on definition 5.15 Basis ¶
      - depends_on definition 5.12 Subspace generated by a set of vectors ¶
      - depends_on definition 5.14 Linear independence ¶
  - depends_on definition 22.14 Phase-space coordinate transformation ¶
    - depends_on definition 22.2 Hamiltonian ¶
      - depends_on definition 21.34 Generalized momentum ¶
      - depends_on definition 21.31 Lagrangian ¶
depends_on equation 22.46 eq:ham-jacobi ¶
depends_on remark 26.7 The regularity assumption, stated once ¶ ↺
proves proof ch:09-constrained-hamiltonian-dynamics@proof-4 ¶

Supports

depends_on proposition 26.43 The hypersurface-deformation algebra ¶
depends_on proposition 26.37 Constraint structure of Yang–Mills theory ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	First and second class	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:357
`depends_on`	→	eq:ham-jacobi	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:357
`depends_on`	→	The regularity assumption, stated once	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:357
`depends_on`	←	The hypersurface-deformation algebra	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:1735
`depends_on`	←	Constraint structure of Yang–Mills theory	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:1438
`proves`	←	ch:09-constrained-hamiltonian-dynamics@proof-4	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:360