definition A.698 The Hertz contact problem

open in the book · appendices/A-long-proofs.tex:33820 · p. 3131

ground object -- no derivation owed

Rests on

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 definition 30.17 Traction ¶
      - depends_on theorem 30.18 Cauchy: the stress tensor exists ¶
      - proves proof ch:13-continuum-elasticity@proof-8 ¶
    - depends_on theorem 5.79 Spectral theorem for a self-adjoint operator ¶
      - depends_on corollary 5.72 Existence of an eigenvalue over $\C$ ¶
      - depends_on definition 5.41 Adjoint ¶
      - depends_on theorem 5.40 Rank–nullity ¶
      - proves proof ch:03-linear-algebra-representations@proof-31 ¶
  - 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 definition 10.1 Partial differential equation; order ¶
      - depends_on definition 6.24 Metric ¶
    - depends_on theorem 30.21 Cauchy's equation of motion ¶
      - depends_on theorem 7.133 Gauss ¶
      - depends_on theorem 30.18 Cauchy: the stress tensor exists ¶ ↺
      - proves proof ch:13-continuum-elasticity@proof-9 ¶
  - 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 ¶ ↺

Supports

depends_on lemma A.700 The displacement produced by an elliptic pressure ¶
- 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 ¶
depends_on proposition A.701 The two-body compliance rule ¶
- depends_on theorem A.702 Hertz's solution ¶ ↺
depends_on remark A.699 The third condition is not decoration ¶
depends_on theorem A.702 Hertz's solution ¶ ↺

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`	→	Hertzian contact	declared	appendices/A-long-proofs.tex:33844
`depends_on`	→	Boussinesq's point-force solution, quoted	declared	appendices/A-long-proofs.tex:33844
`depends_on`	←	The displacement produced by an elliptic pressure	declared	appendices/A-long-proofs.tex:33888
`depends_on`	←	The two-body compliance rule	declared	appendices/A-long-proofs.tex:33984
`depends_on`	←	The third condition is not decoration	declared	appendices/A-long-proofs.tex:33867
`depends_on`	←	Hertz's solution	declared	appendices/A-long-proofs.tex:34031