definition 16.53 Jacobi accessory equation; conjugate point
open in the book ·
parts/02-mathematical-methods/14-calculus-of-variations.tex:1589
· p. 648
- ground object -- no derivation owed
Rests on
- depends_on equation 16.20 eq:calcvar-euler-lagrange ¶
- depends_on equation 16.45 eq:calcvar-second-variation ¶
Supports
- depends_on proposition 23.53 A caustic point is a conjugate point ¶
-
depends_on
theorem A.436
Strengthened Jacobi condition and conjugate points
¶
- depends_on corollary A.445 Displacing the initial point ¶
-
depends_on
theorem 16.55
Jacobi's necessary condition
¶
- depends_on proposition 23.53 A caustic point is a conjugate point ¶ ↺
- depends_on remark 30.54 Other end conditions, and what buckling is variationally ¶
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 |
→ | eq:calcvar-euler-lagrange | declared | parts/02-mathematical-methods/14-calculus-of-variations.tex:1600 |
depends_on |
→ | eq:calcvar-second-variation | declared | parts/02-mathematical-methods/14-calculus-of-variations.tex:1600 |
depends_on |
← | A caustic point is a conjugate point | declared | parts/03-classical-mechanics/06-hamilton-jacobi.tex:1801 |
depends_on |
← | Strengthened Jacobi condition and conjugate points | declared | appendices/A-long-proofs.tex:21486 |
depends_on |
← | Jacobi's necessary condition | declared | parts/02-mathematical-methods/14-calculus-of-variations.tex:1624 |