proposition 30.49 The Rayleigh speed of a Poisson solid

open in the book · parts/03-classical-mechanics/13-continuum-elasticity.tex:1771 · p. 1026

Rests on

depends_on proposition 30.48 Rayleigh's secular equation ¶
- 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 7.98 Functions of class $C^{1}$ ¶
      - depends_on definition 6.2 Open set ¶
    - depends_on definition 6.24 Metric ¶
      - depends_on definition 3.43 Map ¶
      - depends_on definition 3.38 Ordered pair and Cartesian product ¶
  - depends_on theorem 30.21 Cauchy's equation of motion ¶
    - depends_on theorem 7.133 Gauss ¶
      - depends_on definition 7.127 Simple regions ¶
      - depends_on remark 7.128 What the derivations below take as given ¶
      - depends_on theorem 7.43 Fundamental theorem of calculus, II ¶
      - proves proof ch:05-real-analysis@proof-79 ¶
    - 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-9 ¶
- depends_on theorem 30.40 Navier–Cauchy equations ¶
  - depends_on equation 30.21 eq:elast-hooke-isotropic ¶
  - depends_on theorem 30.21 Cauchy's equation of motion ¶ ↺
  - proves proof ch:13-continuum-elasticity@proof-18 ¶
- proves proof ch:13-continuum-elasticity@proof-24 ¶
proves proof ch:13-continuum-elasticity@proof-25 ¶

Supports

depends_on phenomenon 30.47 The three seismic phases ¶

Neighborhood

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Edges

type	direction	node	provenance	where
`depends_on`	→	Rayleigh's secular equation	declared	parts/03-classical-mechanics/13-continuum-elasticity.tex:1780
`depends_on`	←	The three seismic phases	declared	parts/03-classical-mechanics/13-continuum-elasticity.tex:1624
`proves`	←	ch:13-continuum-elasticity@proof-25	declared	parts/03-classical-mechanics/13-continuum-elasticity.tex:1783