phenomenon 30.60 Coulomb's law of torsion

open in the book · parts/03-classical-mechanics/13-continuum-elasticity.tex:2170 · p. 1031

Rests on

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 definition 7.126 Line and surface integrals ¶
      - depends_on definition 30.2 Representative volume element; continuum field ¶
    - depends_on theorem 30.18 Cauchy: the stress tensor exists ¶
      - depends_on definition 30.17 Traction ¶ ↺
      - depends_on definition 13.5 Tensor under orthogonal transformations ¶
      - proves proof ch:13-continuum-elasticity@proof-7 ¶
    - 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 theorem 8.19 Fundamental theorem of algebra ¶
      - depends_on theorem 5.71 The eigenvalues are the roots of the characteristic polynomial ¶
      - proves proof ch:03-linear-algebra-representations@proof-27 ¶
    - depends_on definition 5.41 Adjoint ¶
      - depends_on definition 5.18 Inner product ¶
      - depends_on definition 5.37 Linear transformation ¶
    - depends_on theorem 5.40 Rank–nullity ¶
      - depends_on definition 5.15 Basis ¶
      - depends_on definition 5.39 Kernel, image, nullity, rank ¶
      - depends_on lemma 5.38 Exchange and completion ¶
      - proves proof ch:03-linear-algebra-representations@proof-13 ¶
    - proves proof ch:03-linear-algebra-representations@proof-31 ¶
- depends_on equation 30.21 eq:elast-hooke-isotropic ¶
depends_on equation 30.21 eq:elast-hooke-isotropic ¶ ↺
proves proof ch:13-continuum-elasticity@proof-31 ¶

Supports

depends_on example 30.61 A torsion fibre as a force sensor ¶
depends_on phenomenon 34.3 The stiffness of a twisted wire is geometric ¶
depends_on remark 30.62 Saint-Venant's theory: non-circular sections warp ¶
tests experiment Coulomb: the torsion pendulum ¶

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
`cites`	→	Recherches théoriques et expérimentales sur la force de torsion et sur l'élasticité des fils de métal	derived	parts/03-classical-mechanics/13-continuum-elasticity.tex:2182
`depends_on`	→	The engineering moduli	declared	parts/03-classical-mechanics/13-continuum-elasticity.tex:2186
`depends_on`	→	eq:elast-hooke-isotropic	declared	parts/03-classical-mechanics/13-continuum-elasticity.tex:2186
`depends_on`	←	A torsion fibre as a force sensor	declared	parts/03-classical-mechanics/13-continuum-elasticity.tex:2238
`depends_on`	←	The stiffness of a twisted wire is geometric	declared	parts/03-classical-mechanics/17-exp-pendulum.tex:461
`depends_on`	←	Saint-Venant's theory: non-circular sections warp	declared	parts/03-classical-mechanics/13-continuum-elasticity.tex:2260
`proves`	←	ch:13-continuum-elasticity@proof-31	declared	parts/03-classical-mechanics/13-continuum-elasticity.tex:2189
`tests`	←	Coulomb: the torsion pendulum	declared	parts/03-classical-mechanics/17-exp-pendulum.tex:325