theorem 21.36 Conservation of the conjugate momentum

open in the book · parts/03-classical-mechanics/04-lagrangian-mechanics.tex:951 · p. 786

Rests on

depends_on definition 21.35 Cyclic coordinate ¶
depends_on equation 21.39 eq:lag-el-conservative ¶
depends_on equation 21.43 eq:lag-generalized-momentum ¶
proves proof ch:04-lagrangian-mechanics@proof-8 ¶

Supports

depends_on proposition 23.14 Cyclic coordinates ¶
- depends_on example 23.25 Central force in plane polar coordinates ¶
- depends_on example 23.22 Free particle ¶
  - depends_on remark 23.42 Phase speed and particle speed ¶
- depends_on example 23.27 Charged particle in a uniform magnetic field ¶
- depends_on example 23.23 Uniform gravity, and the parabola ¶
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 ¶

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`	→	Cyclic coordinate	declared	parts/03-classical-mechanics/04-lagrangian-mechanics.tex:954
`depends_on`	→	eq:lag-el-conservative	declared	parts/03-classical-mechanics/04-lagrangian-mechanics.tex:954
`depends_on`	→	eq:lag-generalized-momentum	declared	parts/03-classical-mechanics/04-lagrangian-mechanics.tex:954
`depends_on`	←	Cyclic coordinates	declared	parts/03-classical-mechanics/06-hamilton-jacobi.tex:431
`depends_on`	←	Three first integrals	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:1276
`proves`	←	ch:04-lagrangian-mechanics@proof-8	declared	parts/03-classical-mechanics/04-lagrangian-mechanics.tex:958