definition 18.18 Galilean transformation

open in the book · parts/03-classical-mechanics/01-kinematics.tex:510 · p. 724

ground object -- no derivation owed

Rests on

depends_on definition 18.8 Inertial frame of reference ¶
- depends_on definition 18.7 Frame of reference ¶
  - depends_on definition 18.3 Particle ¶
- 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 ¶

Supports

depends_on proposition 18.20 The Galilean group ¶
- depends_on corollary 18.24 Galilean composition of velocities ¶
  - depends_on phenomenon 18.26 Composition of velocities, and its limit ¶
  - depends_on remark 18.25 Where the additivity goes ¶
- depends_on remark 18.22 Superseded, and in exactly what sense ¶
depends_on proposition 18.21 Galilean invariants ¶
- depends_on remark 18.22 Superseded, and in exactly what sense ¶ ↺
depends_on proposition 18.23 Transformation of velocity and acceleration ¶
- depends_on phenomenon 18.26 Composition of velocities, and its limit ¶ ↺
depends_on proposition 19.13 Which forces are admissible ¶
- depends_on corollary 19.14 Central pair forces are admissible ¶
  - depends_on postulate 19.61 Newton's third law, strong form ¶
    - depends_on theorem 19.63 The spin obeys the same law about the centre of mass ¶
      - depends_on phenomenon 19.65 Spin is conserved when no external torque acts ¶
      - depends_on theorem 19.68 Conservation of angular momentum ¶
    - depends_on theorem 19.62 Rotational second law for a system ¶
      - depends_on theorem 19.68 Conservation of angular momentum ¶ ↺
depends_on remark 18.19 Why the map is affine, and what is assumed to make it so ¶
depends_on remark 19.11 Mass is a Galilean scalar ¶
depends_on theorem 19.12 Galilean covariance of the second law ¶
- depends_on proposition 19.13 Which forces are admissible ¶ ↺
- depends_on theorem 19.25 Galilean covariance of the rotational second law ¶
depends_on theorem 19.25 Galilean covariance of the rotational second law ¶ ↺

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`	→	Inertial frame of reference	declared	parts/03-classical-mechanics/01-kinematics.tex:524
`depends_on`	→	Absolute time	declared	parts/03-classical-mechanics/01-kinematics.tex:524
`depends_on`	→	Principle of Galilean relativity	declared	parts/03-classical-mechanics/01-kinematics.tex:524
`depends_on`	←	The Galilean group	declared	parts/03-classical-mechanics/01-kinematics.tex:575
`depends_on`	←	Galilean invariants	declared	parts/03-classical-mechanics/01-kinematics.tex:644
`depends_on`	←	Transformation of velocity and acceleration	declared	parts/03-classical-mechanics/01-kinematics.tex:709
`depends_on`	←	Which forces are admissible	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:354
`depends_on`	←	Why the map is affine, and what is assumed to make it so	declared	parts/03-classical-mechanics/01-kinematics.tex:547
`depends_on`	←	Mass is a Galilean scalar	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:295
`depends_on`	←	Galilean covariance of the second law	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:304
`depends_on`	←	Galilean covariance of the rotational second law	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:712