theorem A.664 Bertrand's condition

open in the book · appendices/A-long-proofs.tex:32336 · p. 3115

Rests on

depends_on equation A.1059 eq:app-bertrand-linearized ¶
depends_on lemma A.663 Derivatives of the power law ¶
- depends_on equation A.1058 eq:app-bertrand-Jpower ¶
- depends_on equation A.1051 eq:app-bertrand-circular ¶
- proves proof app:A-long-proofs@proof-398 ¶
depends_on proposition A.661 The first-order narrowing ¶
- depends_on equation 27.39 eq:cfs-apsidal-angle ¶
- depends_on lemma A.660 The index in terms of the force ¶
  - depends_on definition A.659 Circular orbit and its index ¶
    - depends_on definition A.658 The orbit function ¶
      - depends_on equation 27.30 eq:cfs-binet-u ¶
      - depends_on equation 19.4 eq:newt-fma ¶
      - depends_on proposition 27.23 Binet equation ¶
    - depends_on equation A.1050 eq:app-bertrand-orbit ¶
  - depends_on equation A.1049 eq:app-bertrand-J ¶
  - proves proof app:A-long-proofs@proof-396 ¶
- proves proof app:A-long-proofs@proof-397 ¶
proves proof app:A-long-proofs@proof-399 ¶

Nothing declares a dependency on this node yet.

Every logical edge within two steps of this node.

type	direction	node	provenance	where
`depends_on`	→	eq:app-bertrand-linearized	declared	appendices/A-long-proofs.tex:32355
`depends_on`	→	Derivatives of the power law	declared	appendices/A-long-proofs.tex:32355
`depends_on`	→	The first-order narrowing	declared	appendices/A-long-proofs.tex:32355
`proves`	←	app:A-long-proofs@proof-399	declared	appendices/A-long-proofs.tex:32359