definition 19.39 Body

open in the book · parts/03-classical-mechanics/02-newtonian-dynamics.tex:1172 · p. 747

ground object -- no derivation owed

Rests on

depends_on definition 18.4 Body ¶
- depends_on definition 18.3 Particle ¶
depends_on definition 19.3 Mass ¶
- depends_on definition 18.3 Particle ¶ ↺
- depends_on postulate 19.1 Inertia ¶
  - 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 definition 18.3 Particle ¶ ↺

Supports

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 19.63 The spin obeys the same law about the centre of mass ¶
- 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 theorem 29.29 Poinsot's construction ¶
    - depends_on example 29.23 The polar moment of the Earth, and what it reveals ¶
      - depends_on phenomenon 29.34 Free nutation of the Earth ¶
    - 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 definition 29.19 Inertia ellipsoid ¶ ↺
      - depends_on theorem 29.16 Principal axes ¶
    - depends_on proposition 29.24 MacCullagh's formula ¶
      - depends_on phenomenon 29.49 Precession of the equinoxes ¶
    - 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 29.11 Angular velocity in Euler angles ¶
      - depends_on remark 29.10 Other conventions, and why the choice must be stated ¶
    - depends_on proposition 125.2 Crystallographic restriction ¶
      - depends_on remark 125.3 What the theorem does and does not forbid ¶
    - depends_on proposition 29.8 Chasles: the general displacement is a screw ¶

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`	→	Body	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1175
`depends_on`	→	Mass	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1175
`depends_on`	←	Position of the centre of mass	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1377
`depends_on`	←	Moment of inertia about an axis	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1225
`depends_on`	←	Total mass	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1187
`depends_on`	←	Rigid body	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:51