definition 19.29 Kinetic energy

open in the book · parts/03-classical-mechanics/02-newtonian-dynamics.tex:808 · p. 742

ground object -- no derivation owed

Rests on

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 7.2 Absolute value ¶
    - depends_on definition 7.9 Real function ¶
      - depends_on definition 3.43 Map ¶
  - 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 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 18.7 Frame of reference ¶ ↺
    - depends_on definition 18.6 Free particle ¶
      - depends_on definition 18.3 Particle ¶ ↺
  - depends_on definition 18.3 Particle ¶ ↺

Supports

depends_on definition 19.31 Energy ¶
- depends_on proposition 27.20 Conservation of energy ¶
- depends_on theorem 19.32 Conservation of energy ¶
  - depends_on phenomenon 50.6 No material surface ¶
  - depends_on phenomenon 19.33 Mechanical energy is conserved ¶
  - depends_on theorem 21.43 Conservation of energy ¶
    - depends_on proposition 29.36 Three first integrals ¶
      - depends_on phenomenon 29.38 Nutation of a released top ¶
      - depends_on proposition 29.43 The three integrable heavy tops ¶
      - depends_on proposition 29.40 The sleeping top ¶
      - depends_on theorem 29.37 Reduction to one degree of freedom ¶
    - depends_on theorem 27.10 Lagrange–Dirichlet ¶
depends_on theorem 19.38 Work–energy theorem ¶

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`	→	Velocity	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:815
`depends_on`	→	Mass	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:815
`depends_on`	←	Energy	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:857
`depends_on`	←	Work–energy theorem	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1132