On the modelling and testing of a laboratory scale Foucault pendulum as a precursor for the design of a high performance measurement instrument

Matthew P. Cartmell, James E. Faller, Nicholas A. Lockerbie, Eva Handous

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Abstract

An integrated study is presented on the dynamic modelling and experimental testing of a mid-length Foucault pendulum with the aim of confirming insights from the literature on the reliable operation of this device and setting markers for future research in which the pendulum may be used for the measurement of relativistic effects due to terrestrial gravity. A tractable nonlinear mathematical model is derived for the dynamics of a practical laboratory Foucault pendulum and its performance with and without parametric excitation, and with coupling to long-axis torsion is investigated numerically for different geographical locations. An experimental pendulum is also tested, with and
without parametric excitation, and it is shown that the model closely predicts the general precessional performance of the pendulum, for the case of applied parametric excitation of the length, when responding to the Newtonian rotation of the Earth. Many of the principal inherent performance limitations of Foucault pendulums from the literature have been confirmed and a general prescription for design is evolved, placing the beneficial effect of principal parametric resonance of this inherently nonlinear system in a central mitigating position, along with other assistive means of response moderation such as excitational phase control through electromagnetic pushing, enclosure, and the minimisation of seismic and EMC noise. It is also shown, through a supporting analysis and calculation, that although the terrestrial measurement of Lense-Thirring precession by means of a Foucault pendulum is certainly still within the realms of possibility there remains a very challenging increase in resolution capability required, in the order of 2*109 to be sure of reliable detection, notwithstanding the removal of extraneous motions and interferences. This study sets the scene for a further investigation in the very near future in which these challenges are to be met, so that a new assault can be made on the terrestrial measurement of Lense-Thirring precession.
Original languageEnglish
Article number20190680
Number of pages26
JournalProceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences
Volume476
Issue number2238
Early online date3 Jun 2020
DOIs
Publication statusPublished - 24 Jun 2020

Keywords

  • Foucault pendulum
  • parametric excitation
  • nonlinear dynamics
  • Lense-Thirring precession
  • general relativity

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    Cartmell, M. P., Faller, J. E., Lockerbie, N. A., & Handous, E. (2020). On the modelling and testing of a laboratory scale Foucault pendulum as a precursor for the design of a high performance measurement instrument. Proceedings of the Royal Society of London Series A - Mathematical Physical and Engineering Sciences, 476(2238), [20190680]. https://doi.org/10.1098/rspa.2019.0680