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Chapter 15Gyroscopes and gravitational wavesDonato Bini 1 and Fernando de Felice 21 Istituto per Applicazioni della Matematica, CNR, I-80131Napoli, Italy and International Center for RelativisticAstrophysics, University of Rome, I-00185 Roma, Italy2 Dipartimento di Fisica ‘G. Galilei’, Università degli Studi diPadova, Via Marzolo, 8, I-35131, Padova, Italy and INFN,Sezione di Padova, ItalyThe behaviour of a gyroscope in geodesic motion is studied in the field ofa plane gravitational wave. We find that, with respect to a special set offrames, the compass of inertia undergoes a precession which, to first order in thedimensionless amplitude h of the wave, is dominated by the cross-polarizationalone. This suggests that a gyro might act as a filter of the polarization state ofthe wave.15.1 IntroductionThe (direct) detection of gravitational waves is still an open question, althoughindirect evidence for their existence has been obtained from the observationof the binary pulsar system PSR 1913+16 [1]. Besides the well-known barantennae, there is a growing interest in laser interferometry detectors, like LIGOand VIRGO, which are sensitive to the low frequency (∼10 Hz) gravitationalwaves which are emitted by sources like coalescing binaries.The purpose of this paper is to study the behaviour of a test gyroscopewhich is acted upon by a plane gravitational wave with the purpose to seewhether this interaction leads to observable effects. It is well known that inthe absence of significant coupling between the background curvature and themultipole moments of the energy–momentum tensor of an extended body, thespin vector is Fermi–Walker transported along the body’s own trajectory (see [2]268