example 26.22 Holonomic constraints

open in the book · parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:696 · p. 907

example -- no derivation owed by its kind

Rests on

depends_on definition 26.20 Dirac bracket ¶
- 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 proposition 26.19 Second-class constraints come in pairs ¶
  - 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 remark 26.7 The regularity assumption, stated once ¶
    - depends_on definition 22.29 Poisson bracket ¶ ↺
  - depends_on proposition 5.119 Normal form of a non-degenerate antisymmetric form ¶
    - depends_on definition 5.110 Bilinear map ¶
      - depends_on definition 5.37 Linear transformation ¶
    - depends_on definition 5.113 Non-degenerate form ¶
      - depends_on definition 5.110 Bilinear map ¶ ↺
    - depends_on definition 5.111 Symmetric and antisymmetric forms ¶
      - depends_on definition 5.110 Bilinear map ¶ ↺
      - depends_on equation 5.137 eq:lin-bilinear-matrix ¶
    - depends_on equation 5.139 eq:lin-bilinear-congruence ¶
    - proves proof ch:03-linear-algebra-representations@proof-54 ¶
  - proves proof ch:09-constrained-hamiltonian-dynamics@proof-7 ¶
depends_on definition 21.2 Holonomic constraint ¶
proves proof ch:09-constrained-hamiltonian-dynamics@proof-9 ¶

Supports

Nothing declares a dependency on this node yet.

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`	→	Dirac bracket	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:705
`depends_on`	→	Holonomic constraint	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:705
`proves`	←	ch:09-constrained-hamiltonian-dynamics@proof-9	declared	parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:708