phenomenon 18.26 Composition of velocities, and its limit

open in the book · parts/03-classical-mechanics/01-kinematics.tex:768 · p. 727

phenomenon-tested: no experiment declares a \tests edge to it and it is not listed in untested.txt

Rests on

depends_on corollary 18.24 Galilean composition of velocities ¶
- depends_on proposition 18.20 The Galilean group ¶
  - depends_on definition 4.73 External semidirect product ¶
    - depends_on definition 4.1 Cartesian product ¶
      - depends_on definition 3.28 Set ¶
    - depends_on definition 4.43 Group homomorphism ¶
      - depends_on definition 4.21 Group ¶
      - depends_on definition 3.43 Map ¶
    - depends_on proposition 4.72 The automorphism group ¶
      - depends_on definition 4.45 Group automorphism ¶
      - depends_on definition 4.36 Subgroup ¶
      - depends_on definition 4.48 Symmetric group ¶
      - proves proof ch:02-algebraic-structures@proof-27 ¶
  - 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 postulate 18.14 Absolute time ¶
    - depends_on postulate 18.16 Principle of Galilean relativity ¶
  - depends_on example 4.78 The Euclidean group ¶
    - depends_on definition 4.73 External semidirect product ¶ ↺
    - depends_on proposition 4.77 When a semidirect product is direct ¶
      - depends_on definition 4.65 Direct product of groups ¶
      - depends_on definition 4.60 Normal subgroup ¶
      - depends_on proposition 4.75 The two factors inside the semidirect product ¶
      - proves proof ch:02-algebraic-structures@proof-31 ¶
  - proves proof ch:01-kinematics@proof-4 ¶
- proves proof ch:01-kinematics@proof-7 ¶
depends_on proposition 18.23 Transformation of velocity and acceleration ¶
- 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 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 13.9 Tangent vector to a curve ¶
      - depends_on definition 13.8 Curve ¶
- depends_on definition 18.18 Galilean transformation ¶ ↺
- depends_on definition 18.10 Velocity ¶ ↺
- proves proof ch:01-kinematics@proof-6 ¶
proves proof ch:01-kinematics@proof-8 ¶

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type	direction	node	provenance	where
`cites`	→	Sur les hypothèses relatives à l'éther lumineux, et sur une expérience qui paraît démontrer que le mouvement des corps change la vitesse avec laquelle la lumière se propage dans leur intérieur	derived	parts/03-classical-mechanics/01-kinematics.tex:779
`cites`	→	On the Relative Motion of the Earth and the Luminiferous Ether	derived	parts/03-classical-mechanics/01-kinematics.tex:777
`depends_on`	→	Galilean composition of velocities	declared	parts/03-classical-mechanics/01-kinematics.tex:780
`depends_on`	→	Transformation of velocity and acceleration	declared	parts/03-classical-mechanics/01-kinematics.tex:780
`proves`	←	ch:01-kinematics@proof-8	declared	parts/03-classical-mechanics/01-kinematics.tex:783