Physical pendulum model: Fractional differential equation and memory effects

Luís Nobre Gonçalves, João C. Fernandes, António Ferraz, Ana Gomes Silva, Pedro José Oliveira Sebastião

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)
30 Downloads (Pure)


A detailed analysis of pendular motion is presented. Inertial effects, self-oscillation, and memory, together with non-constant moment of inertia, hysteresis, and negative damping are shown to be required for the comprehensive description of the free pendulum oscillatory regime. The effects of very high initial amplitudes, friction in the roller bearing axle, drag, and pendulum geometry are also analyzed and discussed. A model consisting of a fractional differential equation fits and explains high resolution and long-time experimental data gathered from standard action-camera videos.

Original languageEnglish
Pages (from-to)962-975
Number of pages14
JournalAmerican Journal Of Physics
Issue number11
Publication statusPublished - 1 Nov 2020


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