experiment Galileo and Huygens: isochronism

open in the book · parts/03-classical-mechanics/17-exp-pendulum.tex:62

citation-roles: 8 of 8 citation(s) carry no role wrapper

Rests on

assumes equation 28.8 eq:osc-pendulum-exact ¶
tests equation 28.7 eq:osc-pendulum-period ¶
tests phenomenon 28.9 Isochronism of the small-amplitude pendulum ¶
- 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 remark 9.3 Normal form and first-order systems ¶
      - depends_on theorem 9.8 Picard–Lindelöf ¶
      - 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

Nothing declares a dependency on this node yet.

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
`assumes`	→	eq:osc-pendulum-exact	declared	parts/03-classical-mechanics/17-exp-pendulum.tex:64
`cites`	→	Discorsi e dimostrazioni matematiche intorno a due nuove scienze	derived	parts/03-classical-mechanics/17-exp-pendulum.tex:79
`cites`	→	Discorsi e dimostrazioni matematiche intorno a due nuove scienze	derived	parts/03-classical-mechanics/17-exp-pendulum.tex:112
`cites`	→	Discorsi e dimostrazioni matematiche intorno a due nuove scienze	derived	parts/03-classical-mechanics/17-exp-pendulum.tex:190
`cites`	→	Discorsi e dimostrazioni matematiche intorno a due nuove scienze	derived	parts/03-classical-mechanics/17-exp-pendulum.tex:316
`cites`	→	Horologium Oscillatorium sive de motu pendulorum ad horologia aptato demonstrationes geometricae	derived	parts/03-classical-mechanics/17-exp-pendulum.tex:89
`cites`	→	Horologium Oscillatorium sive de motu pendulorum ad horologia aptato demonstrationes geometricae	derived	parts/03-classical-mechanics/17-exp-pendulum.tex:116
`cites`	→	Horologium Oscillatorium sive de motu pendulorum ad horologia aptato demonstrationes geometricae	derived	parts/03-classical-mechanics/17-exp-pendulum.tex:214
`cites`	→	Horologium Oscillatorium sive de motu pendulorum ad horologia aptato demonstrationes geometricae	derived	parts/03-classical-mechanics/17-exp-pendulum.tex:316
`tests`	→	eq:osc-pendulum-period	declared	parts/03-classical-mechanics/17-exp-pendulum.tex:63
`tests`	→	Isochronism of the small-amplitude pendulum	declared	parts/03-classical-mechanics/17-exp-pendulum.tex:63