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

M. V. Berry*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)

1 Citation (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 languageEnglish
Article number055007
Number of pages9
JournalEuropean Journal of Physics
Volume39
Issue number5
Early online date12 Jul 2018
DOIs
Publication statusPublished - Sep 2018

Keywords

  • amplification
  • instability
  • pendulum
  • stability

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