theorem 19.58 Decomposition of the angular momentum

open in the book · parts/03-classical-mechanics/02-newtonian-dynamics.tex:1733 · p. 755

Rests on

depends_on definition 19.55 Angular momentum of the centre of mass ¶
- depends_on definition 19.18 Angular momentum ¶
  - depends_on definition 18.3 Particle ¶
  - depends_on definition 19.5 Linear momentum ¶
    - 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 13.9 Tangent vector to a curve ¶
    - depends_on definition 19.3 Mass ¶
      - depends_on definition 18.3 Particle ¶ ↺
      - depends_on postulate 19.1 Inertia ¶
- depends_on definition 19.51 Linear momentum of the centre of mass ¶
  - depends_on definition 19.47 Position of the centre of mass ¶
    - depends_on definition 19.39 Body ¶
      - depends_on definition 18.4 Body ¶
      - depends_on definition 19.3 Mass ¶ ↺
    - depends_on definition 19.40 Total mass ¶
      - depends_on definition 19.39 Body ¶ ↺
      - depends_on definition 19.3 Mass ¶ ↺
  - depends_on definition 19.5 Linear momentum ¶ ↺
depends_on equation 19.44 eq:newt-cm-momentum ¶
depends_on lemma 19.57 The centre of mass is the origin of its own frame ¶
- depends_on equation 19.38 eq:newt-cm-position ¶
- depends_on equation 19.49 eq:newt-cm-relative ¶
- proves proof ch:02-newtonian-dynamics@proof-18 ¶
proves proof ch:02-newtonian-dynamics@proof-19 ¶

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Angular momentum of the centre of mass	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1745
`depends_on`	→	eq:newt-cm-momentum	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1745
`depends_on`	→	The centre of mass is the origin of its own frame	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1745
`depends_on`	←	The spin obeys the same law about the centre of mass	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1893
`proves`	←	ch:02-newtonian-dynamics@proof-19	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1749