theorem 16.97 Equivalence with Newton's second law
open in the book ·
parts/02-mathematical-methods/14-calculus-of-variations.tex:3090
· p. 665
Rests on
- 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 ¶
Supports
- depends_on definition 28.3 Simple harmonic oscillator ¶
- depends_on proposition 19.71 The Newtonian closed system is a Lagrangian system ¶
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-system | declared | parts/02-mathematical-methods/14-calculus-of-variations.tex:3100 |
depends_on |
→ | eq:calcvar-hamilton-action | declared | parts/02-mathematical-methods/14-calculus-of-variations.tex:3100 |
depends_on |
← | Simple harmonic oscillator | declared | parts/03-classical-mechanics/11-oscillations-waves.tex:101 |
depends_on |
← | The Newtonian closed system is a Lagrangian system | declared | parts/03-classical-mechanics/02-newtonian-dynamics.tex:2180 |
proves |
← | ch:14-calculus-of-variations@proof-46 | declared | parts/02-mathematical-methods/14-calculus-of-variations.tex:3104 |