remark A.690 Poisson's count, and why it cannot be right

open in the book · appendices/A-long-proofs.tex:33548 · p. 3128

remark -- no derivation owed by its kind

Rests on

depends_on definition A.689 Edge resultants ¶
- depends_on equation A.1110 eq:app-kirchhoff-moments ¶
- depends_on proposition A.682 The plane-stress law ¶
  - depends_on definition 30.63 Flexural rigidity ¶
    - depends_on proposition 30.33 Conversion among the moduli ¶
      - depends_on definition 30.31 The engineering moduli ¶
      - depends_on phenomenon 30.32 Poisson contraction ¶
      - proves proof ch:13-continuum-elasticity@proof-15 ¶
    - depends_on proposition 30.51 Moment and curvature ¶
      - depends_on definition 30.31 The engineering moduli ¶ ↺
      - depends_on equation 30.21 eq:elast-hooke-isotropic ¶
      - proves proof ch:13-continuum-elasticity@proof-27 ¶
  - depends_on equation 30.21 eq:elast-hooke-isotropic ¶ ↺
  - depends_on proposition 30.33 Conversion among the moduli ¶ ↺
  - proves proof app:A-long-proofs@proof-405 ¶
depends_on theorem A.688 The Kirchhoff plate equation ¶
- depends_on lemma A.687 Kinetic energy ¶
  - depends_on definition A.680 Kirchhoff kinematics ¶
    - depends_on definition 30.6 Linear strain and infinitesimal rotation ¶
      - depends_on definition 13.91 Symmetric and antisymmetric parts ¶
      - depends_on equation 30.2 eq:elast-displacement ¶
    - depends_on proposition 30.51 Moment and curvature ¶ ↺
  - proves proof app:A-long-proofs@proof-408 ¶
- depends_on lemma 16.18 Fundamental lemma ¶
  - depends_on definition 16.15 Variation; the first variation ¶
    - depends_on definition 16.11 Admissible class; functional ¶
      - depends_on definition 7.98 Functions of class $C^{1}$ ¶
      - depends_on theorem 7.40 Continuous functions are integrable ¶
    - depends_on equation 7.177 eq:ana-functional-derivative ¶
  - depends_on theorem 7.40 Continuous functions are integrable ¶ ↺
  - proves proof ch:14-calculus-of-variations@proof-8 ¶
- depends_on proposition A.684 The plate energy ¶
  - depends_on definition 30.63 Flexural rigidity ¶ ↺
  - depends_on lemma A.681 Strains under the Kirchhoff hypothesis ¶
    - depends_on definition A.680 Kirchhoff kinematics ¶ ↺
    - depends_on definition 30.6 Linear strain and infinitesimal rotation ¶ ↺
    - proves proof app:A-long-proofs@proof-404 ¶
  - depends_on proposition A.682 The plane-stress law ¶ ↺
  - proves proof app:A-long-proofs@proof-406 ¶
- proves proof app:A-long-proofs@proof-409 ¶

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`	→	Edge resultants	declared	appendices/A-long-proofs.tex:33563
`depends_on`	→	The Kirchhoff plate equation	declared	appendices/A-long-proofs.tex:33563