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

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

Towards a high-performance Foucault pendulum for the measurement of relativistic gravity

The Foucault pendulum has become one of the fundamental experiments of physics since Léon Foucault's famous demonstration of a 67 metre pendulum with a 22 kg bob mass at the Panthéon in Paris in 1851. This paper attempts to show that Foucault's fundamental experiment could perhaps be developed into a highly sensitive measurement system capable of resolving the tiny precessional motions of relativistic frame-dragging. The authors have shown that their mathematical model of a Foucault pendulum performs extremely well in terms of predicting the Newtonian rotation of the Earth. The model takes account of latitude and incorporates parametric excitation of the length as a harmonic modulating motion of ≤ 0.01 of the nominal pendulum length. The main aim of the ongoing work discussed in this paper is to try to resolve the tiny motions of Lense-Thirring frame-dragging precession, for which we confirm that a first approximation prediction at a chosen terrestrial latitude can be obtained through an analogy between Maxwellian electrodynamics and gravitoelectromagnetism. A new experimental measurement will require an increase in resolution of at least 2 × 10' over that required for measuring the Newtonian rotation of the Earth

First narrow-band search for continuous gravitational waves from known pulsars in advanced detector data

International audienceSpinning neutron stars asymmetric with respect to their rotation axis are potential sources of continuous gravitational waves for ground-based interferometric detectors. In the case of known pulsars a fully coherent search, based on matched filtering, which uses the position and rotational parameters obtained from electromagnetic observations, can be carried out. Matched filtering maximizes the signal-to-noise (SNR) ratio, but a large sensitivity loss is expected in case of even a very small mismatch between the assumed and the true signal parameters. For this reason, narrow-band analysis methods have been developed, allowing a fully coherent search for gravitational waves from known pulsars over a fraction of a hertz and several spin-down values. In this paper we describe a narrow-band search of 11 pulsars using data from Advanced LIGO’s first observing run. Although we have found several initial outliers, further studies show no significant evidence for the presence of a gravitational wave signal. Finally, we have placed upper limits on the signal strain amplitude lower than the spin-down limit for 5 of the 11 targets over the bands searched; in the case of J1813-1749 the spin-down limit has been beaten for the first time. For an additional 3 targets, the median upper limit across the search bands is below the spin-down limit. This is the most sensitive narrow-band search for continuous gravitational waves carried out so far