proposition 30.12 The Green strain measures length exactly
open in the book ·
parts/03-classical-mechanics/13-continuum-elasticity.tex:334
· p. 1011
Rests on
-
depends_on
definition 30.11
Green strain
¶
-
depends_on
definition 30.6
Linear strain and infinitesimal rotation
¶
- depends_on definition 13.91 Symmetric and antisymmetric parts ¶
- depends_on equation 30.2 eq:elast-displacement ¶
- depends_on equation 30.2 eq:elast-displacement ¶ ↺
-
depends_on
definition 30.6
Linear strain and infinitesimal rotation
¶
-
depends_on
definition 13.118
Line element
¶
-
depends_on
definition 13.117
Metric tensor of signature $(p,q)$
¶
-
depends_on
definition 13.48
Differentiable manifold
¶
- depends_on definition 13.47 Differentiable structure ¶
-
depends_on
definition 13.84
Tensor
¶
-
depends_on
definition 13.83
Covector
¶
- depends_on definition 13.81 Vector on a manifold ¶
- depends_on definition 13.81 Vector on a manifold ¶ ↺
-
depends_on
definition 13.83
Covector
¶
-
depends_on
definition 13.48
Differentiable manifold
¶
-
depends_on
definition 13.117
Metric tensor of signature $(p,q)$
¶
- proves proof ch:13-continuum-elasticity@proof-4 ¶
Supports
- depends_on example 30.13 A rigid rotation forges a strain of $-\theta^{2}/2$ ¶
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 |
→ | Green strain | declared | parts/03-classical-mechanics/13-continuum-elasticity.tex:342 |
depends_on |
→ | Line element | declared | parts/03-classical-mechanics/13-continuum-elasticity.tex:342 |
depends_on |
← | A rigid rotation forges a strain of $-\theta^{2}/2$ | declared | parts/03-classical-mechanics/13-continuum-elasticity.tex:384 |
proves |
← | ch:13-continuum-elasticity@proof-4 | declared | parts/03-classical-mechanics/13-continuum-elasticity.tex:345 |