proposition A.701 The two-body compliance rule

open in the book · appendices/A-long-proofs.tex:33968 · p. 3133

Rests on

depends_on definition A.698 The Hertz contact problem ¶
- depends_on phenomenon 30.70 Hertzian contact ¶
  - depends_on definition 30.31 The engineering moduli ¶
    - depends_on definition 30.20 Pressure and deviatoric stress ¶
      - depends_on proposition 30.19 The stress tensor is symmetric ¶
      - depends_on theorem 5.79 Spectral theorem for a self-adjoint operator ¶
    - depends_on equation 30.21 eq:elast-hooke-isotropic ¶
  - depends_on proposition 30.23 Virtual work; the weak form ¶
    - depends_on definition 30.22 Boundary conditions of elastostatics ¶
      - depends_on definition 10.24 Well-posed problem ¶
      - depends_on theorem 30.21 Cauchy's equation of motion ¶
    - depends_on theorem 30.21 Cauchy's equation of motion ¶ ↺
    - proves proof ch:13-continuum-elasticity@proof-10 ¶
  - proves proof ch:13-continuum-elasticity@proof-34 ¶
  - proves proof ch:13-continuum-elasticity@prooflink-3 ¶
- depends_on theorem A.695 Boussinesq's point-force solution, quoted ¶
  - depends_on definition 30.31 The engineering moduli ¶ ↺
  - depends_on equation 30.21 eq:elast-hooke-isotropic ¶ ↺
  - depends_on theorem 30.18 Cauchy: the stress tensor exists ¶
    - depends_on definition 30.17 Traction ¶
      - depends_on definition 7.126 Line and surface integrals ¶
      - depends_on definition 30.2 Representative volume element; continuum field ¶
    - depends_on definition 13.5 Tensor under orthogonal transformations ¶
      - depends_on definition 13.4 Orthogonal coordinate transformation ¶
    - proves proof ch:13-continuum-elasticity@proof-7 ¶
depends_on lemma A.697 Surface displacement under a distributed pressure ¶
- depends_on theorem A.695 Boussinesq's point-force solution, quoted ¶ ↺
- proves proof app:A-long-proofs@proof-411 ¶
proves proof app:A-long-proofs@proof-413 ¶

Supports

depends_on theorem A.702 Hertz's solution ¶
- depends_on example A.703 The numbers of the chapter, recomputed ¶
- depends_on remark A.704 $E^{*}$ in two roles, and one trap ¶
- depends_on remark A.705 The dangerous stress is below the surface ¶

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`	→	The Hertz contact problem	declared	appendices/A-long-proofs.tex:33984
`depends_on`	→	Surface displacement under a distributed pressure	declared	appendices/A-long-proofs.tex:33984
`depends_on`	←	Hertz's solution	declared	appendices/A-long-proofs.tex:34031
`proves`	←	app:A-long-proofs@proof-413	declared	appendices/A-long-proofs.tex:33987