proposition 18.23 Transformation of velocity and acceleration

open in the book · parts/03-classical-mechanics/01-kinematics.tex:694 · p. 726

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 18.18 Galilean transformation ¶
- depends_on definition 18.8 Inertial frame of reference ¶
  - depends_on definition 18.7 Frame of reference ¶ ↺
  - depends_on definition 18.6 Free particle ¶
    - depends_on definition 18.3 Particle ¶ ↺
- depends_on postulate 18.14 Absolute time ¶
- depends_on postulate 18.16 Principle of Galilean relativity ¶
depends_on definition 18.10 Velocity ¶ ↺
proves proof ch:01-kinematics@proof-6 ¶

Supports

depends_on phenomenon 18.26 Composition of velocities, and its limit ¶

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:709
`depends_on`	→	Galilean transformation	declared	parts/03-classical-mechanics/01-kinematics.tex:709
`depends_on`	→	Velocity	declared	parts/03-classical-mechanics/01-kinematics.tex:709
`depends_on`	←	Composition of velocities, and its limit	declared	parts/03-classical-mechanics/01-kinematics.tex:780
`proves`	←	ch:01-kinematics@proof-6	declared	parts/03-classical-mechanics/01-kinematics.tex:713