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

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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 minimization of seismic and EMC noise. It is also shown, through a supporting analysis and calculation, that although the terrestrial measurement of the Lense–Thirring (LT) 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 × 10 9 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 LT precession.

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          Foucault Pendulum at the South Pole: Proposal For an Experiment to Detect the Earth's General Relativistic Gravitomagnetic Field

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            The precessing spherical pendulum

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              The Parametrically Maintained Foucault Pendulum and Its Perturbations

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                Author and article information

                Journal
                Proc Math Phys Eng Sci
                Proc. Math. Phys. Eng. Sci
                RSPA
                royprsa
                Proceedings. Mathematical, Physical, and Engineering Sciences
                The Royal Society Publishing
                1364-5021
                1471-2946
                June 2020
                3 June 2020
                3 June 2020
                : 476
                : 2238
                : 20190680
                Affiliations
                [1 ]Aerospace Centre of Excellence, Department of Mechanical and Aerospace Engineering, University of Strathclyde , Glasgow G1 1XJ, UK
                [2 ]JILA, University of Colorado , Boulder, CO 80309, USA
                [3 ]Institute for Gravitational Research, School of Physics and Astronomy, College of Science and Engineering, University of Glasgow , Glasgow G12 8QQ, UK
                [4 ]Emeritus Professor of Physics, University of Strathclyde , Glasgow G4 0NG, UK
                [5 ]Ecole Nationale Supérieure d'Arts et Métiers , Campus de Lille, 8 Boulevard Louis XIV, 59000 Lille, France
                Author notes

                Electronic supplementary material is available online at https://doi.org/10.6084/m9.figshare.c.4984886.

                Author information
                http://orcid.org/0000-0002-3982-6315
                Article
                rspa20190680
                10.1098/rspa.2019.0680
                7428043
                1cb8cf60-3a4c-4d71-bffc-b7aaf8d23bbc
                © 2020 The Authors.

                Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.

                History
                : 23 October 2019
                : 1 May 2020
                Funding
                Funded by: University of Strathclyde, http://dx.doi.org/10.13039/100008078;
                Award ID: Feasibility Study Programme Award
                Categories
                1009
                122
                162
                120
                Research Article
                Custom metadata
                June, 2020

                Physics
                foucault pendulum,parametric excitation,nonlinear dynamics,lense–thirring precession,general relativity

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