proposition 19.71 The Newtonian closed system is a Lagrangian system

open in the book · parts/03-classical-mechanics/02-newtonian-dynamics.tex:2166 · p. 759

Rests on

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 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 postulate 19.6 Newton's first law ¶
    - 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 19.5 Linear momentum ¶ ↺
depends_on equation 19.4 eq:newt-fma ¶
depends_on theorem 16.97 Equivalence with Newton's second law ¶
- depends_on equation 16.30 eq:calcvar-euler-lagrange-system ¶
- depends_on equation 16.86 eq:calcvar-hamilton-action ¶
- proves proof ch:14-calculus-of-variations@proof-46 ¶
proves proof ch:02-newtonian-dynamics@proof-27 ¶

Nothing declares a dependency on this node yet.

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	Conservative force and potential energy	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:2180
`depends_on`	→	eq:newt-fma	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:2180
`depends_on`	→	Equivalence with Newton's second law	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:2180
`proves`	←	ch:02-newtonian-dynamics@proof-27	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:2184