theorem 19.32 Conservation of energy

open in the book · parts/03-classical-mechanics/02-newtonian-dynamics.tex:872 · p. 743

Rests on

depends_on definition 19.31 Energy ¶
- depends_on definition 19.30 Conservative force and potential energy ¶
  - depends_on equation 19.2 eq:newt-second-law ¶
  - depends_on postulate 19.8 Newton's second law ¶
    - depends_on definition 19.5 Linear momentum ¶
      - depends_on definition 18.10 Velocity ¶
      - depends_on definition 19.3 Mass ¶
    - 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 ¶ ↺
- depends_on definition 19.29 Kinetic energy ¶
  - depends_on definition 18.10 Velocity ¶ ↺
  - depends_on definition 19.3 Mass ¶ ↺
depends_on equation 19.19 eq:newt-conservative ¶
depends_on equation 19.4 eq:newt-fma ¶
proves proof ch:02-newtonian-dynamics@proof-9 ¶

Supports

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 remark 29.45 What integrability buys, and where it stops ¶
    - depends_on remark 29.44 The Kovalevskaya integral ¶
  - depends_on proposition 29.40 The sleeping top ¶
  - depends_on theorem 29.37 Reduction to one degree of freedom ¶
    - depends_on phenomenon 29.38 Nutation of a released top ¶ ↺
    - depends_on proposition 29.40 The sleeping top ¶ ↺
    - depends_on remark 29.42 The closed form, and the mathematics it needs ¶
- depends_on theorem 27.10 Lagrange–Dirichlet ¶

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`	→	Energy	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:887
`depends_on`	→	eq:newt-conservative	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:887
`depends_on`	→	eq:newt-fma	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:887
`depends_on`	←	No material surface	declared	parts/05-general-relativity-cosmology/09-exp-black-holes.tex:915
`depends_on`	←	Mechanical energy is conserved	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:956
`depends_on`	←	Conservation of energy	declared	parts/03-classical-mechanics/04-lagrangian-mechanics.tex:1175
`proves`	←	ch:02-newtonian-dynamics@proof-9	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:890