postulate 19.22 Newton's second law, rotational case

open in the book · parts/03-classical-mechanics/02-newtonian-dynamics.tex:586 · p. 740

ground object -- no derivation owed

Rests on

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 7.16 Limit ¶
      - depends_on definition 7.9 Real function ¶
    - depends_on definition 18.9 Position ¶
      - depends_on definition 18.7 Frame of reference ¶
      - depends_on definition 18.3 Particle ¶ ↺
    - depends_on definition 13.9 Tangent vector to a curve ¶
      - depends_on definition 13.8 Curve ¶
  - 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 18.3 Particle ¶ ↺
depends_on postulate 19.8 Newton's second law ¶
- depends_on definition 19.5 Linear momentum ¶ ↺
- depends_on postulate 19.6 Newton's first law ¶
  - depends_on definition 18.8 Inertial frame of reference ¶ ↺
  - depends_on definition 19.5 Linear momentum ¶ ↺

Supports

depends_on theorem 29.25 Euler's equations ¶
- depends_on phenomenon 29.46 A fast spinning top does not fall ¶
  - depends_on phenomenon 29.49 Precession of the equinoxes ¶
    - depends_on proposition 29.50 The principal nutation ¶
- depends_on phenomenon 29.31 The intermediate-axis instability ¶
  - depends_on remark 29.32 What the linearization is entitled to conclude ¶
- depends_on proposition 29.26 The two integrals of torque-free motion ¶
  - depends_on proposition 29.33 Dissipation drives a free body to its largest moment ¶
  - depends_on proposition 29.43 The three integrable heavy tops ¶
    - depends_on remark 29.45 What integrability buys, and where it stops ¶
    - depends_on remark 29.44 The Kovalevskaya integral ¶
  - depends_on remark 29.27 Euler's equations as a Lie–Poisson system ¶
  - depends_on remark 29.30 Polhode and herpolhode ¶
  - depends_on remark 24.42 The intermediate axis ¶
  - depends_on theorem 29.29 Poinsot's construction ¶
    - depends_on remark 29.32 What the linearization is entitled to conclude ¶ ↺
    - depends_on remark 29.30 Polhode and herpolhode ¶ ↺
- depends_on proposition 29.28 Free rotation of a symmetric body ¶
  - depends_on phenomenon 29.34 Free nutation of the Earth ¶
- depends_on proposition 24.41 The free rigid body is a Lie–Poisson system ¶
  - depends_on remark 24.48 Reduction is what physicists do without saying so ¶
    - depends_on example A.573 The abelian case, and eliminating a cyclic coordinate ¶
  - depends_on remark 24.42 The intermediate axis ¶ ↺

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`	→	Angular momentum	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:590
`depends_on`	→	Newton's second law	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:590
`depends_on`	←	Euler's equations	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:752