definition 18.7 Frame of reference

open in the book · parts/03-classical-mechanics/01-kinematics.tex:149 · p. 719

ground object -- no derivation owed

Rests on

depends_on definition 18.3 Particle ¶

Supports

depends_on definition 18.8 Inertial frame of reference ¶
- depends_on definition 27.16 Areal velocity ¶
- depends_on definition 18.18 Galilean transformation ¶
  - 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    - depends_on remark 18.22 Superseded, and in exactly what sense ¶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    - depends_on remark 18.22 Superseded, and in exactly what sense ¶ ↺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 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 ¶ ↺
- depends_on phenomenon 18.17 Uniform motion is undetectable from within ¶
  - depends_on remark 18.13 Absolute space is stated here, and not adopted ¶
- depends_on postulate 19.6 Newton's first law ¶
  - depends_on phenomenon 19.7 Persistence of uniform motion ¶
  - depends_on postulate 19.19 Newton's first law, rotational case ¶
    - depends_on phenomenon 19.21 Equal areas in equal times ¶
    - depends_on proposition 20.13 Eastward deflection of a body dropped from rest ¶
      - depends_on remark 20.14 Why the elementary argument gives three halves of this ¶
  - depends_on postulate 19.8 Newton's second law ¶
    - depends_on definition 19.30 Conservative force and potential energy ¶
      - depends_on definition 27.13 Central force ¶
      - depends_on definition 19.31 Energy ¶
      - depends_on proposition 19.71 The Newtonian closed system is a Lagrangian system ¶
    - depends_on definition 19.34 Work ¶
      - depends_on definition 19.35 Power ¶
      - depends_on proposition 19.36 Work of a torque ¶
      - depends_on theorem 19.38 Work–energy theorem ¶
    - depends_on phenomenon 49.16 Pulsars: clocks at nuclear density ¶
    - depends_on phenomenon 42.1 Universality of free fall ¶
      - depends_on phenomenon 53.5 Universality of free fall, as measured ¶
      - depends_on phenomenon 42.4 The lunar orbit is not polarized toward the Sun ¶
    - depends_on phenomenon 19.10 Force, mass and acceleration ¶
    - depends_on postulate 19.22 Newton's second law, rotational case ¶
      - depends_on theorem 29.25 Euler's equations ¶
    - depends_on postulate 19.48 Newton's third law ¶
      - depends_on phenomenon 19.50 Recoil and the conservation of momentum ¶
      - depends_on postulate 19.49 Net internal force ¶
      - depends_on postulate 19.61 Newton's third law, strong form ¶ ↺
      - depends_on theorem 27.30 Reduction of the two-body problem ¶
      - depends_on theorem 19.52 The centre of mass moves as a particle ¶
    - depends_on theorem 20.2 Parabolic trajectory ¶
      - depends_on corollary 20.3 Range, apex, time of flight ¶
      - depends_on phenomenon 20.6 Air drag ¶
      - depends_on remark 20.5 rem:projectile-idealisation ¶
    - depends_on theorem 29.51 Equation of motion in a rotating frame ¶
      - depends_on phenomenon 42.4 The lunar orbit is not polarized toward the Sun ¶ ↺
  - depends_on proposition 19.20 For one particle the rotational first law is not independent ¶
- depends_on postulate 19.1 Inertia ¶
  - depends_on definition 19.2 Interaction ¶
    - depends_on postulate 19.48 Newton's third law ¶ ↺
  - depends_on definition 19.3 Mass ¶
    - depends_on definition 19.39 Body ¶
      - depends_on definition 19.47 Position of the centre of mass ¶
      - depends_on definition 19.41 Moment of inertia about an axis ¶
      - depends_on definition 19.40 Total mass ¶
      - depends_on definition 29.1 Rigid body ¶
    - depends_on definition 19.29 Kinetic energy ¶
      - depends_on definition 19.31 Energy ¶ ↺
      - depends_on theorem 19.38 Work–energy theorem ¶ ↺
    - depends_on definition 19.41 Moment of inertia about an axis ¶ ↺
    - depends_on definition 19.5 Linear momentum ¶
      - depends_on definition 27.2 Translational equilibrium ¶
      - depends_on definition 19.18 Angular momentum ¶
      - depends_on definition 19.51 Linear momentum of the centre of mass ¶
      - depends_on postulate 19.6 Newton's first law ¶ ↺
      - depends_on postulate 19.8 Newton's second law ¶ ↺
    - depends_on definition 19.40 Total mass ¶ ↺
    - depends_on remark 19.11 Mass is a Galilean scalar ¶ ↺
depends_on definition 18.1 Motion and rest ¶
depends_on definition 18.9 Position ¶
- depends_on definition 18.27 Angular position, velocity and acceleration ¶
  - depends_on definition 18.29 Angular velocity vector ¶
    - depends_on remark 18.30 The angular velocity is an element of $\mathfrak{so}(3)$ ¶
  - depends_on phenomenon 18.31 Uniform circular motion is accelerated motion ¶
    - depends_on proposition 18.32 Tangential and centripetal components ¶
  - depends_on proposition 18.32 Tangential and centripetal components ¶ ↺
  - depends_on remark 18.28 The radian carries no dimension ¶
- depends_on definition 18.1 Motion and rest ¶ ↺
- depends_on definition 18.10 Velocity ¶
  - depends_on definition 18.11 Acceleration ¶
    - depends_on definition 18.27 Angular position, velocity and acceleration ¶ ↺
    - depends_on lemma 27.15 Velocity and acceleration in plane polar coordinates ¶
    - depends_on phenomenon 18.31 Uniform circular motion is accelerated motion ¶ ↺
    - depends_on phenomenon 18.12 Uniformly accelerated motion ¶
      - depends_on phenomenon 20.1 phen:parabolic-trajectory ¶
    - 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 18.23 Transformation of velocity and acceleration ¶ ↺
  - depends_on definition 18.27 Angular position, velocity and acceleration ¶ ↺
  - depends_on definition 18.29 Angular velocity vector ¶ ↺
  - depends_on definition 19.29 Kinetic energy ¶ ↺
  - depends_on definition 19.5 Linear momentum ¶ ↺
  - depends_on lemma 27.15 Velocity and acceleration in plane polar coordinates ¶ ↺
  - depends_on proposition 18.23 Transformation of velocity and 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`	→	Particle	declared	parts/03-classical-mechanics/01-kinematics.tex:152
`depends_on`	←	Inertial frame of reference	declared	parts/03-classical-mechanics/01-kinematics.tex:174
`depends_on`	←	Motion and rest	declared	parts/03-classical-mechanics/01-kinematics.tex:47
`depends_on`	←	Position	declared	parts/03-classical-mechanics/01-kinematics.tex:193