definition 18.4 Body

open in the book · parts/03-classical-mechanics/01-kinematics.tex:126 · p. 718

ground object -- no derivation owed

Rests on

depends_on definition 18.3 Particle ¶

Supports

depends_on definition 19.39 Body ¶
- depends_on definition 19.47 Position of the centre of mass ¶
  - depends_on definition 27.6 Centre of gravity ¶
  - depends_on definition 19.51 Linear momentum of the centre of mass ¶
    - depends_on definition 19.55 Angular momentum of the centre of mass ¶
      - depends_on proposition 29.14 Angular momentum and kinetic energy ¶
      - depends_on theorem 19.58 Decomposition of the angular momentum ¶
  - depends_on theorem 29.20 Parallel-axis theorem ¶
    - depends_on corollary 29.21 The centre of mass minimizes the moment ¶
- depends_on definition 19.41 Moment of inertia about an axis ¶
  - depends_on definition 19.42 Inertia tensor ¶
    - depends_on definition 29.13 Inertia tensor, continuum form ¶
      - depends_on definition 29.19 Inertia ellipsoid ¶
      - depends_on example 29.23 The polar moment of the Earth, and what it reveals ¶
      - depends_on proposition 49.17 Magnetic-dipole spin-down ¶
      - depends_on proposition 29.14 Angular momentum and kinetic energy ¶ ↺
      - depends_on proposition 29.15 Positivity ¶
      - depends_on proposition 29.24 MacCullagh's formula ¶
      - depends_on proposition 29.22 Perpendicular-axis theorem ¶
      - depends_on theorem 29.20 Parallel-axis theorem ¶ ↺
      - depends_on theorem 29.16 Principal axes ¶
    - depends_on example 19.45 The uniform solid sphere ¶
    - depends_on proposition 19.43 The moment of inertia is a quadratic form in the axis ¶
  - depends_on theorem 19.44 Parallel axes; Steiner ¶
- depends_on definition 19.40 Total mass ¶
  - depends_on definition 19.47 Position of the centre of mass ¶ ↺
- depends_on definition 29.1 Rigid body ¶
  - depends_on proposition 29.2 Six degrees of freedom ¶
    - depends_on theorem 29.3 Euler's rotation theorem ¶
      - depends_on notation 29.9 The $z$–$x$–$z$ Euler angles used in this treatise ¶
      - depends_on proposition 125.2 Crystallographic restriction ¶
      - depends_on proposition 29.8 Chasles: the general displacement is a screw ¶
depends_on remark 18.5 rem:kin-body-refined ¶

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:128
`depends_on`	←	Body	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1175
`depends_on`	←	rem:kin-body-refined	declared	parts/03-classical-mechanics/01-kinematics.tex:135