phenomenon 28.9 Isochronism of the small-amplitude pendulum

open in the book · parts/03-classical-mechanics/11-oscillations-waves.tex:238 · p. 947

Rests on

depends_on equation 28.2 eq:osc-sho ¶
depends_on proposition 28.4 General solution and isochronism ¶
- 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 ¶
      - 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 ¶
proves proof ch:11-oscillations-waves@proof-4 ¶

Supports

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
`cites`	→	Discorsi e dimostrazioni matematiche intorno a due nuove scienze	derived	parts/03-classical-mechanics/11-oscillations-waves.tex:247
`depends_on`	→	eq:osc-sho	declared	parts/03-classical-mechanics/11-oscillations-waves.tex:252
`depends_on`	→	General solution and isochronism	declared	parts/03-classical-mechanics/11-oscillations-waves.tex:252
`assumes`	←	Kater: the reversible pendulum	declared	parts/03-classical-mechanics/17-exp-pendulum.tex:794
`proves`	←	ch:11-oscillations-waves@proof-4	declared	parts/03-classical-mechanics/11-oscillations-waves.tex:255
`tests`	←	Galileo and Huygens: isochronism	declared	parts/03-classical-mechanics/17-exp-pendulum.tex:63