proposition 18.33 Intrinsic decomposition of the acceleration

open in the book · parts/03-classical-mechanics/01-kinematics.tex:1013 · p. 730

Rests on

depends_on definition 18.11 Acceleration ¶
- depends_on definition 7.26 Derivative of a function at a point ¶
  - depends_on definition 7.16 Limit ¶
    - depends_on definition 7.2 Absolute value ¶
    - depends_on definition 7.9 Real function ¶
      - depends_on definition 3.43 Map ¶
  - depends_on definition 7.9 Real function ¶ ↺
- depends_on definition 18.10 Velocity ¶
  - depends_on definition 7.26 Derivative of a function at a point ¶ ↺
  - depends_on definition 18.9 Position ¶
    - depends_on definition 18.7 Frame of reference ¶
      - depends_on definition 18.3 Particle ¶
    - depends_on definition 18.3 Particle ¶ ↺
  - depends_on definition 13.9 Tangent vector to a curve ¶
    - depends_on definition 13.8 Curve ¶
depends_on definition 13.14 Principal unit normal vector ¶
- depends_on definition 13.13 Normal curvature vector of a curve ¶
  - depends_on definition 13.12 Unit tangent vector ¶
    - 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 13.9 Tangent vector to a curve ¶ ↺
depends_on definition 13.12 Unit tangent vector ¶ ↺
proves proof ch:01-kinematics@proof-11 ¶

Supports

depends_on remark 18.34 The two ways an acceleration can be zero ¶

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`	→	Acceleration	declared	parts/03-classical-mechanics/01-kinematics.tex:1033
`depends_on`	→	Principal unit normal vector	declared	parts/03-classical-mechanics/01-kinematics.tex:1033
`depends_on`	→	Unit tangent vector	declared	parts/03-classical-mechanics/01-kinematics.tex:1033
`depends_on`	←	The two ways an acceleration can be zero	declared	parts/03-classical-mechanics/01-kinematics.tex:1081
`proves`	←	ch:01-kinematics@proof-11	declared	parts/03-classical-mechanics/01-kinematics.tex:1037