equation 27.30 eq:cfs-binet-u

open in the book · parts/03-classical-mechanics/10-central-forces-statics.tex:716

part of a statement or proof

Rests on

step_from equation 27.29 eq:cfs-binet-phidot ¶
step_from equation 27.16 eq:cfs-polar-acceleration ¶

Supports

depends_on definition A.658 The orbit function ¶
- depends_on definition A.659 Circular orbit and its index ¶
  - depends_on lemma A.660 The index in terms of the force ¶
    - depends_on proposition A.661 The first-order narrowing ¶
      - depends_on theorem A.664 Bertrand's condition ¶
step_from equation 27.46 eq:cfs-orbit-ode ¶

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
`step_from`	→	eq:cfs-binet-phidot	declared — eliminating $t$ in favour of $\phi$ through $\dot\phi=Lu^{2}/m$ and writing $u=1/r$	parts/03-classical-mechanics/10-central-forces-statics.tex:721
`step_from`	→	eq:cfs-polar-acceleration	declared — eliminating $t$ in favour of $\phi$ through $\dot\phi=Lu^{2}/m$ and writing $u=1/r$	parts/03-classical-mechanics/10-central-forces-statics.tex:721
`depends_on`	←	The orbit function	declared	appendices/A-long-proofs.tex:32139
`step_from`	←	eq:cfs-orbit-ode	declared — substituting $f=-ku^{2}$ and cancelling the common factor $u^{2}$	parts/03-classical-mechanics/10-central-forces-statics.tex:1081