definition 13.12 Unit tangent vector

open in the book · parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:691 · p. 458

ground object -- no derivation owed

Rests on

depends_on definition 13.11 Arc length ¶
- depends_on definition 13.8 Curve ¶
- depends_on definition 13.9 Tangent vector to a curve ¶
  - depends_on definition 13.8 Curve ¶ ↺
depends_on definition 13.9 Tangent vector to a curve ¶ ↺

Supports

depends_on definition 13.15 Unit binormal vector ¶
depends_on definition 13.13 Normal curvature vector of a curve ¶
- depends_on definition 13.36 Geodesic curvature vector ¶
  - depends_on definition 13.37 Geodesic lines ¶
- depends_on definition 13.28 Normal curvature vector of a surface ¶
  - depends_on definition 13.29 Gaussian curvature ¶
    - depends_on theorem 13.30 Theorema Egregium; Gauss, 1827 ¶
      - depends_on corollary 13.31 Bending invariance ¶
  - depends_on definition 13.36 Geodesic curvature vector ¶ ↺
- depends_on definition 13.14 Principal unit normal vector ¶
  - depends_on definition 13.15 Unit binormal vector ¶ ↺
  - depends_on proposition 18.33 Intrinsic decomposition of the acceleration ¶
    - depends_on remark 18.34 The two ways an acceleration can be zero ¶
depends_on proposition 18.33 Intrinsic decomposition of the acceleration ¶ ↺

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`	→	Arc length	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:696
`depends_on`	→	Tangent vector to a curve	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:696
`depends_on`	←	Unit binormal vector	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:746
`depends_on`	←	Normal curvature vector of a curve	declared	parts/02-mathematical-methods/11-manifolds-tensors-curvature.tex:706
`depends_on`	←	Intrinsic decomposition of the acceleration	declared	parts/03-classical-mechanics/01-kinematics.tex:1033