phenomenon 34.3 The stiffness of a twisted wire is geometric

open in the book · parts/03-classical-mechanics/17-exp-pendulum.tex:451 · p. 1142

phenomenon-tested: no experiment declares a \tests edge to it and it is not listed in untested.txt

Rests on

depends_on equation 30.55 eq:elast-torsion-constant ¶
depends_on phenomenon 30.60 Coulomb's law of torsion ¶
- 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 equation 30.21 eq:elast-hooke-isotropic ¶ ↺
- proves proof ch:13-continuum-elasticity@proof-31 ¶
proves proof ch:17-exp-pendulum@proof-2 ¶

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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/17-exp-pendulum.tex:456
`depends_on`	→	eq:elast-torsion-constant	declared	parts/03-classical-mechanics/17-exp-pendulum.tex:461
`depends_on`	→	Coulomb's law of torsion	declared	parts/03-classical-mechanics/17-exp-pendulum.tex:461
`proves`	←	ch:17-exp-pendulum@proof-2	declared	parts/03-classical-mechanics/17-exp-pendulum.tex:464