Pumping a swing revisited: Minimal model for parametric resonance via matrix products

M. V. Berry

doi:10.1088/1361-6404/aace82

Pumping a swing revisited: Minimal model for parametric resonance via matrix products

M. V. Berry^*

^*Corresponding author for this work

School of Physics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

3 Citations (Scopus)

Abstract

A child rises on a swing by changing the length of its chain. This is explained by the mathematical fact that the product of two elliptic symplectic matrices can be hyperbolic. The connection could be helpful in teaching both mechanics and matrices. A Hamiltonian formulation avoids an error. Random swinging is unlikely to succeed.

Original language	English
Article number	055007
Number of pages	9
Journal	European Journal of Physics
Volume	39
Issue number	5
Early online date	12 Jul 2018
DOIs	https://doi.org/10.1088/1361-6404/aace82
Publication status	Published - Sept 2018

Keywords

amplification
instability
pendulum
stability

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title = "Pumping a swing revisited: Minimal model for parametric resonance via matrix products",

abstract = "A child rises on a swing by changing the length of its chain. This is explained by the mathematical fact that the product of two elliptic symplectic matrices can be hyperbolic. The connection could be helpful in teaching both mechanics and matrices. A Hamiltonian formulation avoids an error. Random swinging is unlikely to succeed.",

keywords = "amplification, instability, pendulum, stability",

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KW - instability

KW - pendulum

KW - stability

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M3 - Article (Academic Journal)

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ER -

Pumping a swing revisited: Minimal model for parametric resonance via matrix products

Abstract

Keywords

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