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R. Soc. A."],"published-print":{"date-parts":[[2020,6]]},"abstract":"<jats:p>\n                    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\u2013Thirring (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\u2009\u00d7\u200910\n                    <jats:sup>9<\/jats:sup>\n                    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.\n                  <\/jats:p>","DOI":"10.1098\/rspa.2019.0680","type":"journal-article","created":{"date-parts":[[2020,6,3]],"date-time":"2020-06-03T04:13:17Z","timestamp":1591157597000},"page":"20190680","update-policy":"https:\/\/doi.org\/10.1098\/crossmark-policy","source":"Crossref","is-referenced-by-count":9,"title":["On the modelling and testing of a laboratory-scale Foucault pendulum as a precursor for\u00a0the design of a high-performance measurement instrument"],"prefix":"10.1098","volume":"476","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3982-6315","authenticated-orcid":true,"given":"Matthew P.","family":"Cartmell","sequence":"first","affiliation":[{"name":"Aerospace Centre of Excellence, Department of Mechanical and Aerospace Engineering, University of Strathclyde, Glasgow G1 1XJ, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"James E.","family":"Faller","sequence":"additional","affiliation":[{"name":"JILA, University of Colorado, Boulder, CO 80309, USA"},{"name":"Institute for Gravitational Research, School of Physics and Astronomy, College of Science and Engineering, University of Glasgow, Glasgow G12 8QQ, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nicholas A.","family":"Lockerbie","sequence":"additional","affiliation":[{"name":"Institute for Gravitational Research, School of Physics and Astronomy, College of Science and Engineering, University of Glasgow, Glasgow G12 8QQ, UK"},{"name":"Emeritus Professor of Physics, University of Strathclyde, Glasgow G4 0NG, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eva","family":"Handous","sequence":"additional","affiliation":[{"name":"Ecole Nationale Sup\u00e9rieure d'Arts et M\u00e9tiers, Campus de Lille, 8 Boulevard Louis XIV, 59000 Lille, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"175","published-online":{"date-parts":[[2020,6,3]]},"reference":[{"key":"e_1_3_6_2_2","unstructured":"Schumacher RA Tarbet B. 2009 A short Foucault pendulum free of ellipsoidal precession. arXiv:0902.1829v2."},{"key":"e_1_3_6_3_2","first-page":"241","article-title":"On the irregularities of motion of the Foucault pendulum","volume":"13","author":"Longden AC","year":"1919","journal-title":"Phys. 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See https:\/\/doi.org\/10.17868\/71740."},{"key":"e_1_3_6_29_2","unstructured":"Ruggiero ML Tartaglia A. 2008 Gravitometric effects. arXiv:gr-qc\/0207065v2."}],"container-title":["Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/royalsocietypublishing.org\/doi\/pdf\/10.1098\/rspa.2019.0680","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/royalsocietypublishing.org\/doi\/full-xml\/10.1098\/rspa.2019.0680","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/royalsocietypublishing.org\/doi\/pdf\/10.1098\/rspa.2019.0680","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T21:24:07Z","timestamp":1778621047000},"score":1,"resource":{"primary":{"URL":"http:\/\/royalsocietypublishing.org\/rspa\/article\/80710"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6]]},"references-count":28,"journal-issue":{"issue":"2238","published-print":{"date-parts":[[2020,6]]}},"alternative-id":["10.1098\/rspa.2019.0680"],"URL":"https:\/\/doi.org\/10.1098\/rspa.2019.0680","relation":{},"ISSN":["1364-5021","1471-2946"],"issn-type":[{"value":"1364-5021","type":"print"},{"value":"1471-2946","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,6]]},"assertion":[{"value":"2019-10-23","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2020-05-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2020-06-03","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}