proposition 28.4 General solution and isochronism

open in the book · parts/03-classical-mechanics/11-oscillations-waves.tex:104 · p. 946

Rests on

depends_on equation 28.2 eq:osc-sho ¶
depends_on theorem 9.13 Dimension of the solution space ¶
- depends_on corollary 9.9 Linear equations: existence on the whole interval ¶
  - depends_on definition 9.2 Linear equation; homogeneity ¶
    - depends_on definition 9.1 Ordinary differential equation ¶
  - depends_on remark 9.3 Normal form and first-order systems ¶
  - depends_on theorem 9.8 Picard–Lindelöf ¶
    - depends_on definition 9.4 Lipschitz condition ¶
    - depends_on equation 9.3 eq:slt-ode-system ¶
    - depends_on lemma 9.6 Weierstrass $M$-test; uniform limits are continuous ¶
      - depends_on definition 7.20 Continuity at a point ¶
      - depends_on proposition 7.47 Comparison; absolute convergence ¶
      - proves proof ch:07-odes-sturm-liouville@proof-1 ¶
    - proves proof ch:07-odes-sturm-liouville@proof-2 ¶
  - proves proof ch:07-odes-sturm-liouville@proof-3 ¶
- depends_on definition 9.2 Linear equation; homogeneity ¶ ↺
- proves proof ch:07-odes-sturm-liouville@proof-6 ¶
proves proof ch:11-oscillations-waves@proof-1 ¶

Supports

depends_on phenomenon 28.9 Isochronism of the small-amplitude pendulum ¶
- assumes experiment Kater: the reversible pendulum ¶
- tests experiment Galileo and Huygens: isochronism ¶

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:osc-sho	declared	parts/03-classical-mechanics/11-oscillations-waves.tex:113
`depends_on`	→	Dimension of the solution space	declared	parts/03-classical-mechanics/11-oscillations-waves.tex:113
`depends_on`	←	Isochronism of the small-amplitude pendulum	declared	parts/03-classical-mechanics/11-oscillations-waves.tex:252
`proves`	←	ch:11-oscillations-waves@proof-1	declared	parts/03-classical-mechanics/11-oscillations-waves.tex:116