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Showing papers by "Harald Lück published in 2004"


Journal ArticleDOI
B. P. Abbott1, Richard J. Abbott1, Rana X. Adhikari2, A. Ageev3  +420 moreInstitutions (57)
TL;DR: For 17 days in August and September 2002, the LIGO and GEO interferometer gravitational wave detectors were operated in coincidence to produce their first data for scientific analysis.
Abstract: For 17 days in August and September 2002, the LIGO and GEO interferometer gravitational wave detectors were operated in coincidence to produce their first data for scientific analysis. Although the detectors were still far from their design sensitivity levels, the data can be used to place better upper limits on the flux of gravitational waves incident on the earth than previous direct measurements. This paper describes the instruments and the data in some detail, as a companion to analysis papers based on the first data.

268 citations


Journal ArticleDOI
B. P. Abbott1, R. Abbott1, Rana X. Adhikari2, A. Ageev3  +373 moreInstitutions (34)
TL;DR: In this article, a model emission mechanism is used to interpret the limits as a constraint on the pulsar's equatorial ellipticity, and two independent analysis methods are used and are demonstrated in two independent methods: a frequency domain method and a time domain method.
Abstract: Data collected by the GEO 600 and LIGO interferometric gravitational wave detectors during their first observational science run were searched for continuous gravitational waves from the pulsar J1939+2134 at twice its rotation frequency. Two independent analysis methods were used and are demonstrated in this paper: a frequency domain method and a time domain method. Both achieve consistent null results, placing new upper limits on the strength of the pulsar’s gravitational wave emission. A model emission mechanism is used to interpret the limits as a constraint on the pulsar’s equatorial ellipticity.

172 citations


Journal ArticleDOI
B. P. Abbott1, R. Abbott1, Rana X. Adhikari2, A. Ageev3  +385 moreInstitutions (37)
TL;DR: In this paper, a search for gravitational wave bursts using data from the first science run of the Laser Interferometer Gravitational Wave Observatory (LIGO) detectors was reported. But their search focused on bursts with durations ranging from 4 to 100 ms, and with significant power in the LIGO sensitivity band of 150 to 3000 Hz.
Abstract: We report on a search for gravitational wave bursts using data from the first science run of the Laser Interferometer Gravitational Wave Observatory (LIGO) detectors. Our search focuses on bursts with durations ranging from 4 to 100 ms, and with significant power in the LIGO sensitivity band of 150 to 3000 Hz. We bound the rate for such detected bursts at less than 1.6 events per day at a 90% confidence level. This result is interpreted in terms of the detection efficiency for ad hoc waveforms (Gaussians and sine Gaussians) as a function of their root-sum-square strain hrss; typical sensitivities lie in the range hrss∼10-19–10-17strain/√Hz, depending on the waveform. We discuss improvements in the search method that will be applied to future science data from LIGO and other gravitational wave detectors.

109 citations


Journal ArticleDOI
B. P. Abbott1, Richard J. Abbott1, Rana X. Adhikari2, A. Ageev3  +385 moreInstitutions (37)
TL;DR: In this article, the authors present the analysis of between 50 and 100 h of coincident interferometric strain data used to search for and establish an upper limit on a stochastic background of gravitational radiation.
Abstract: We present the analysis of between 50 and 100 h of coincident interferometric strain data used to search for and establish an upper limit on a stochastic background of gravitational radiation. These data come from the first LIGO science run, during which all three LIGO interferometers were operated over a 2-week period spanning August and September of 2002. The method of cross correlating the outputs of two interferometers is used for analysis. We describe in detail practical signal processing issues that arise when working with real data, and we establish an observational upper limit on a f^-3 power spectrum of gravitational waves. Our 90% confidence limit is Ω0h100(^2)<~23±4.6 in the frequency band 40–314 Hz, where h100 is the Hubble constant in units of 100 km/sec/Mpc and Ω0 is the gravitational wave energy density per logarithmic frequency interval in units of the closure density. This limit is approximately 104 times better than the previous, broadband direct limit using interferometric detectors, and nearly 3 times better than the best narrow-band bar detector limit. As LIGO and other worldwide detectors improve in sensitivity and attain their design goals, the analysis procedures described here should lead to stochastic background sensitivity levels of astrophysical interest.

102 citations


Journal ArticleDOI
TL;DR: FINESSE as mentioned in this paper is a software simulation tool that allows one to compute the optical properties of laser interferometers used by interferometric gravitational-wave detectors, including power enhancement, error and control signals, transfer functions and shot-noise-limited sensitivities.
Abstract: FINESSE is a software simulation allowing one to compute the optical properties of laser interferometers used by interferometric gravitational-wave detectors today. This fast and versatile tool has already proven to be useful in the design and commissioning of gravitational-wave detectors. The basic algorithm of FINESSE numerically computes the light amplitudes inside an interferometer using Hermite–Gauss modes in the frequency domain. In addition, FINESSE provides a number of commands for easily generating and plotting the most common signals including power enhancement, error and control signals, transfer functions and shot-noise-limited sensitivities. Among the various simulation tools available to the gravitational wave community today, FINESSE provides an advanced and versatile optical simulation based on a general analysis of user-defined optical setups and is quick to install and easy to use.

96 citations


Journal ArticleDOI
TL;DR: The GEO 600 laser interferometer with 600 m armlength is currently being commissioned as a part of a worldwide network of gravitational wave detectors as discussed by the authors, and the performance of the detector as of November 2003 is described.
Abstract: The GEO 600 laser interferometer with 600 m armlength is currently being commissioned as a part of a worldwide network of gravitational wave detectors. Due to the use of advanced technologies such as signal recycling and multiple pendulum suspensions with a monolithic last stage the anticipated sensitivity of GEO 600 is close to the initial sensitivity of km baseline detectors. This paper describes the status of the detector as of November 2003 with special emphasis on its performance during the first serious data-taking periods and on the experimental challenges encountered during the commissioning of the dual-recycled detector.

85 citations


Journal ArticleDOI
TL;DR: In this paper, the interference quality at the output of the German/British GEO 600 gravitational-wave detector could be improved with a simple ring heater, where a mismatch of the radii of curvature of the mirrors in the arms of an interferometric GEO detector can be partly compensated by creating a thermal gradient inside the mirror.
Abstract: A mismatch of the radii of curvature of the mirrors in the arms of an interferometric gravitational-wave detector can be partly compensated by creating a thermal gradient inside the mirror. This paper shows how the interference quality at the output of the German/British GEO 600 gravitational-wave detector could be improved with a simple ring heater.

52 citations


Journal ArticleDOI
TL;DR: In this paper, the last of the final interferometer optics of GEO 600 were monolithically suspended, using fused silica fibres, and a corrective coating was applied to some fibres to compensate for the frequency spread due to the tension spread of the four fibres within a suspension.
Abstract: High Q mirror suspensions are a key element of the advanced interferometric gravitational-wave detectors. In December 2002 the last of the final interferometer optics of GEO 600 were monolithically suspended, using fused silica fibres. The violin modes of the suspension fibres can have Q greater than 108 and can therefore interfere with the interferometer length control servo. Hence, the violin modes need to be damped, without degrading the pendulum Q itself. Furthermore, the frequency spread of the fibres used has to be small to allow for high Q notch filtering in the length control servo. The requirements for the violin modes of the two GEO 600 inboard suspensions are Q < 3 × 106 for the fundamental and Q < 2 × 106 for the first harmonic mode, respectively. The frequency spread should not exceed 10% within one mode. To accomplish that, two sections of the fibres were coated with amorphous Teflon. By applying the coating, the Q of the relevant modes can be degraded to the desired values and furthermore, the frequencies of these modes can be tuned almost independently with a good accuracy over a wide range. After welding the fibres in the monolithic suspension, a corrective coating was applied to some fibres, to compensate for the frequency spread due to the tension spread of the four fibres within a suspension. We present the method and the results achieved.

31 citations


Journal ArticleDOI
TL;DR: In this paper, internal mode quality factor measurements of three monolithically suspended test masses are used to estimate the level of internal thermal noise in the GEO 600 interferometer, which is expected to be a limiting noise source in the most sensitive frequency band.
Abstract: Internal thermal noise is expected to be a limiting noise source in the most sensitive frequency band of the GEO 600 gravitational wave detector. Because thermal noise is directly related to energy dissipation, care has been taken to construct test mass suspensions from low-dissipation materials and to eliminate inter-material rubbing where possible. Recently, the GEO 600 team finished the installation of triple-pendulum suspensions for the optics of the Michelson interferometer. Each of these triple pendulums incorporates a monolithic fused silica pendulum as the lowest stage. We have made internal mode quality factor measurements of three monolithically suspended test masses. Using these measurements we estimate of the level of internal thermal noise in the GEO 600 interferometer.

27 citations


Journal ArticleDOI
TL;DR: In this paper, an overview of the automatic mirror alignment system of the GEO 600 detector is presented, which can achieve continuous lock stretches of more than 121 hours duration with a power-recycled Michelson interferometer.
Abstract: We give an overview of the automatic mirror alignment system of the gravitational wave detector GEO 600. In order to achieve the required sensitivity of the Michelson interferometer, the axes of interfering beams have to be superimposed with a residual angle of the order 10 −8 rad. The beam spots have to be centred on the mirrors to minimize coupling of alignment noise into longitudinal signals. We present the actual control topology and results from the system in operation, which controls all alignment degrees of the power-recycled Michelson. With this system continuous lock stretches of more than 121 h duration were achieved.

18 citations


Journal ArticleDOI
J. R. Smith1, Benjamin William Allen1, Peter Aufmuth1, C. Aulbert1, Stanislav Babak2, R. Balasubramanian2, B. Barr3, S. Berukoff1, A. Bunkowski1, Gianpietro Cagnoli3, C. A. Cantley3, Morag M. Casey3, Simon Chelkowski1, D. Churches2, Thomas Cokelaer2, C. N. Colacino1, David Crooks3, Curt Cutler1, Karsten Danzmann1, R. Davies2, R. J. Dupuis3, E. J. Elliffe3, Carsten Fallnich, Alexander Franzen1, Andreas Freise1, Stefan Goßler1, A. Grant3, Hartmut Grote1, S. Grunewald1, Jan Harms1, Gerhard Heinzel1, Ik Siong Heng1, A. Hepstonstall3, M. Heurs1, Martin Hewitson3, Stefan Hild1, J. H. Hough3, Yousuke Itoh1, Roger Jones3, S. H. Huttner3, K. Kawabe1, Christian J. Killow3, Karsten Kötter1, Badri Krishnan1, V. Leonhardt1, Harald Lück1, B. Machenschalk1, M. Malec1, R. A. Mercer4, C. Messenger4, Soumya D. Mohanty1, Kasem Mossavi1, Soma Mukherjee1, P. G. Murray3, Shigeo Nagano1, G. P. Newton3, Maria Alessandra Papa1, Michael Perreur-Lloyd3, Matthew Pitkin3, M. V. Plissi3, V. Quetschke1, V. Re4, Stuart Reid3, L. Ribichini1, D. I. Robertson3, N. A. Robertson3, Joseph D. Romano2, Sheila Rowan3, Albrecht Rüdiger1, Bangalore Suryanarayana Sathyaprakash2, Roland Schilling1, Roman Schnabel1, Bernard F. Schutz1, Frank Seifert1, A. M. Sintes5, Peter H. Sneddon3, Kenneth A. Strain3, Ian Taylor2, R Taylor3, Andre Thüring1, Carlo Ungarelli4, H. Vahlbruch1, Alberto Vecchio4, John Veitch3, H. Ward3, U. Weiland1, Herbert Welling, P. Williams1, Benno Willke1, Walter Winkler1, Graham Woan3, I. Zawischa 
TL;DR: The German-British laser-interferometric gravitational-wave detector GEO 600 is currently being commissioned as part of a worldwide network of gravitational wave detectors as mentioned in this paper, which employs dual recycling-an optical configuration that combines power recycling and signal recycling.
Abstract: The German-British laser-interferometric gravitational-wave detector GEO 600 is currently being commissioned as part of a worldwide network of gravitational-wave detectors. GEO 600 recently became the first kilometre-scale interferometer to employ dual recycling-an optical configuration that combines power recycling and signal recycling. We present a brief overview of the commissioning of this dual-recycled interferometer, the performance results achieved during a subsequent extended data-taking period, and the plans intended to bring GEO 600 to its final configuration.

Journal ArticleDOI
TL;DR: An online, time-domain calibration scheme that was initially developed to calibrate the power-recycled GEO 600 configuration, has been extended to cover the significantly more complicated case of calibrating the dual-cycled interferometer where the optical response of the instrument is much more difficult to measure and calibrate out online as discussed by the authors.
Abstract: The GEO 600 interferometric gravitational detector took part in an extended coincident science run of the LIGO Scientific Collaboration (S3) that started in November 2003. GEO had recently been upgraded to be the first large-scale fully suspended dual-recycled interferometer in the world and was in the early stages of commissioning in this configuration. In order to prepare the GEO 600 data for the possible extraction of science results and for exchange between analysis groups of the gravitational wave community, the data need to be accurately calibrated. An online, time-domain calibration scheme that was initially developed to calibrate the power-recycled GEO 600 configuration, has been extended to cover the significantly more complicated case of calibrating the dual-recycled interferometer, where the optical response of the instrument is much more difficult to measure and calibrate out online. This report presents an overview of this calibration scheme as it was applied to calibrating the GEO S3 science run data. In addition, results of the calibration process are presented together with some discussion of the accuracy achieved.

Journal ArticleDOI
TL;DR: The sensing system, the control topology, and the performance of the automatic alignment system for the two suspended, triangular mode-cleaner cavities of the gravitational wave detector GEO 600 are described.
Abstract: The automatic alignment system for the two suspended, triangular mode-cleaner cavities of the gravitational wave detector GEO 600 has been in continuous operation since the spring of 2001. A total of 20 angular degrees of freedom are controlled by feedback loops with almost no manual alignment having been required since installation. Error signals for the eight most important degrees of freedom are obtained with the differential wave-front sensing technique. We describe the sensing system, the control topology, and the performance of the automatic alignment system. A continuous locking stretch of more than 120 h has been achieved.

Journal ArticleDOI
Benjamin William Allen1, Graham Woan2, B. P. Abbott3, R. Abbott3  +378 moreInstitutions (36)
TL;DR: The first science run of the LIGO and GEO gravitational wave detectors presented the opportunity to test methods of searching for gravitational waves from known pulsars as discussed by the authors, and they presented new direct upper limits on the strength of waves from the pulsar PSR J1939+2134 using two independent analysis methods.
Abstract: The first science run of the LIGO and GEO gravitational wave detectors presented the opportunity to test methods of searching for gravitational waves from known pulsars. Here we present new direct upper limits on the strength of waves from the pulsar PSR J1939+2134 using two independent analysis methods, one in the frequency domain using frequentist statistics and one in the time domain using Bayesian inference. Both methods show that the strain amplitude at Earth from this pulsar is less than a few times 10−22.

Journal ArticleDOI
TL;DR: In this paper, the thermal noise of the pendulum mode of a suspended mirror was analyzed by interferometrically detecting the differential movement of two mirrors suspended as multiple-stage pendulums.
Abstract: To analyse the thermal noise of the pendulum mode of a suspended mirror, we interferometrically detect the differential movement of two mirrors suspended as multiple-stage pendulums. We present the set-up of this experiment and the current sensitivity, and also the different steps that we took in the past to increase the sensitivity, which include an auto alignment of the laser beam into the resonator eigenmode, changes of the seismic isolation system to more damping stages and higher moments of inertia and an intensive noise hunting.

Proceedings ArticleDOI
Hartmut Grote1, Benjamin William Allen1, Peter Aufmuth1, C. Aulbert1, S. Babak1, R. Balasubramanian2, B. Barr3, S. Berukoff1, A. Bunkowski1, Gianpietro Cagnoli3, C. A. Cantley3, Morag M. Casey3, Simon Chelkowski1, D. Churches2, Thomas Cokelaer2, C. N. Colacino1, David Crooks3, Curt Cutler1, Karsten Danzmann1, R. Davies2, R. J. Dupuis3, E. J. Elliffe3, Carsten Fallnich, Alexander Franzen1, Andreas Freise1, Stefan Goßler1, A. Grant3, S. Grunewald1, Jan Harms1, Gerhard Heinzel1, Ik Siong Heng1, A. Hepstonstall3, M. Heurs1, Martin Hewitson1, Stefan Hild1, J. H. Hough3, Yousuke Itoh1, Roger Jones1, S. H. Huttner3, K. Kawabe1, Christian J. Killow3, Karsten Kötter1, Badri Krishnan1, V. Leonhardt1, Harald Lück1, B. Machenschalk1, M. Malec1, R. A. Mercer4, C. Messenger1, Soumya D. Mohanty1, Kasem Mossavi1, Soma Mukherjee1, P. G. Murray3, Shigeo Nagano1, G. P. Newton3, Maria Alessandra Papa1, Michael Perreur-Lloyd3, Matthew Pitkin3, M. V. Plissi3, V. Quetschke1, V. Re4, Stuart Reid3, L. Ribichini1, D. I. Robertson3, N. A. Robertson3, N. A. Robertson5, Joseph D. Romano2, Sheila Rowan3, Albrecht Rüdiger1, Bangalore Suryanarayana Sathyaprakash2, Roland Schilling1, Roman Schnabel1, Bernard F. Schutz1, Frank Seifert1, Alicia M. Sintes1, J. R. Smith1, Peter H. Sneddon3, Kenneth A. Strain3, Ian Taylor2, Richard J. K. Taylor3, Andre Thüring1, Carlo Ungarelli4, Henning Vahlbruch1, Alberto Vecchio4, John Veitch1, H. Ward3, U. Weiland1, Herbert Welling, P. Williams1, Benno Willke1, Walter Winkler1, Graham Woan3, I. Zawischa 
TL;DR: In this article, the authors present a brief overview of the GEO 600 detector, the implementation of dual recycling, and summarize recent work regarding the increase in the detector's sensitivity.
Abstract: Since December 2003, the gravitational-wave detector GEO 600 has routinely operated in the dual recycled mode, using a lock acquisition scheme based on the detection of optical sideband power at the dark port. With the detector locking very robustly, the current commissioning work is entirely dedicated to sensitivity improvements. We give a brief overview of the GEO 600 detector, the implementation of dual recycling, and summarize recent work regarding the increase in the detector sensitivity.

B. P. Abbott, F. Abbott, Rana X. Adhikari, A. Ageev  +370 moreInstitutions (1)
01 Jan 2004
TL;DR: B. Abbott, R. Amin, S. Ito, Y. Itoh, M. Hrynevych, o W. Johnston, A. Klarmane, C. Gosler, P. Gretarsson, D. Guenther, E. Hefetz, G. Frey, L. Hennessy, N. Gillespie, m K. Heptonstall, M K. Hindman, J.
Abstract: B. Abbott, R. Abbott, R. Adhikari, A. Ageev, 28 B. Allen, R. Amin, S. B. Anderson, W. G. Anderson, M. Araya, H. Armandula, F. Asiri, a P. Aufmuth, C. Aulbert, S. Babak, R. Balasubramanian, S. Ballmer, B. C. Barish, D. Barker, C. Barker-Patton, M. Barnes, B. Barr, M. A. Barton, K. Bayer, R. Beausoleil, b K. Belczynski, R. Bennett, c S. J. Berukoff, d J. Betzwieser, B. Bhawal, I. A. Bilenko, G. Billingsley, E. Black, K. Blackburn, B. Bland-Weaver, B. Bochner, e L. Bogue, R. Bork, S. Bose, P. R. Brady, V. B. Braginsky, J. E. Brau, D. A. Brown, S. Brozek, f A. Bullington, A. Buonanno, g R. Burgess, D. Busby, W. E. Butler, R. L. Byer, L. Cadonati, G. Cagnoli, J. B. Camp, C. A. Cantley, L. Cardenas, K. Carter, M. M. Casey, J. Castiglione, A. Chandler, J. Chapsky, h P. Charlton, S. Chatterji, Y. Chen, V. Chickarmane, D. Chin, N. Christensen, D. Churches, C. Colacino, 2 R. Coldwell, M. Coles, i D. Cook, T. Corbitt, D. Coyne, J. D. E. Creighton, T. D. Creighton, D. R. M. Crooks, P. Csatorday, B. J. Cusack, C. Cutler, E. D’Ambrosio, K. Danzmann, 2, 20 R. Davies, E. Daw, j D. DeBra, T. Delker, k R. DeSalvo, S. Dhurandhar, M. Diaz, H. Ding, R. W. P. Drever, R. J. Dupuis, C. Ebeling, J. Edlund, P. Ehrens, E. J. Elliffe, T. Etzel, M. Evans, T. Evans, C. Fallnich, D. Farnham, M. M. Fejer, M. Fine, L. S. Finn, E. Flanagan, A. Freise, l R. Frey, P. Fritschel, V. Frolov, M. Fyffe, K. S. Ganezer, J. A. Giaime, A. Gillespie, m K. Goda, G. Gonzalez, S. Gosler, P. Grandclement, A. Grant, C. Gray, A. M. Gretarsson, D. Grimmett, H. Grote, S. Grunewald, M. Guenther, E. Gustafson, n R. Gustafson, W. O. Hamilton, M. Hammond, J. Hanson, C. Hardham, G. Harry, A. Hartunian, J. Heefner, Y. Hefetz, G. Heinzel, I. S. Heng, M. Hennessy, N. Hepler, A. Heptonstall, M. Heurs, M. Hewitson, N. Hindman, P. Hoang, J. Hough, M. Hrynevych, o W. Hua, R. Ingley, M. Ito, Y. Itoh, A. Ivanov, O. Jennrich, p W. W. Johnson, W. Johnston, L. Jones, D. Jungwirth, q V. Kalogera, E. Katsavounidis, K. Kawabe, 2 S. Kawamura, W. Kells, J. Kern, A. Khan, S. Killbourn, C. J. Killow, C. Kim, C. King, P. King, S. Klimenko, P. Kloevekorn, S. Koranda, K. Kotter, J. Kovalik, D. Kozak, B. Krishnan, M. Landry, J. Langdale, B. Lantz, R. Lawrence, A. Lazzarini, M. Lei, V. Leonhardt, I. Leonor, K. Libbrecht, P. Lindquist, S. Liu, J. Logan, r M. Lormand, M. Lubinski, H. Luck, 2 T. T. Lyons, r B. Machenschalk, M. MacInnis, M. Mageswaran, K. Mailand, W. Majid, h M. Malec, F. Mann, A. Marin, s S. Marka, E. Maros, J. Mason, t K. Mason, O. Matherny, L. Matone, N. Mavalvala, R. McCarthy, D. E. McClelland, M. McHugh, P. McNamara, u G. Mendell, S. Meshkov, C. Messenger, V. P. Mitrofanov, G. Mitselmakher, R. Mittleman, O. Miyakawa, S. Miyoki, v S. Mohanty, w G. Moreno, K. Mossavi, B. Mours, x G. Mueller, S. Mukherjee, w J. Myers, S. Nagano, T. Nash, y H. Naundorf, R. Nayak, G. Newton, F. Nocera, P. Nutzman, T. Olson, B. O’Reilly, D. J. Ottaway, A. Ottewill, z D. Ouimette, q H. Overmier, B. J. Owen, M. A. Papa, C. Parameswariah, V. Parameswariah, M. Pedraza, S. Penn, M. Pitkin, M. Plissi, M. Pratt, V. Quetschke, F. Raab, H. Radkins, R. Rahkola, M. Rakhmanov, S. R. Rao, D. Redding, h M. W. Regehr, h T. Regimbau, K. T. Reilly, K. Reithmaier, D. H. Reitze, S. Richman, aa R. Riesen, K. Riles, A. Rizzi, bb D. I. Robertson, N. A. Robertson, 27 L. Robison, S. Roddy, J. Rollins, J. D. Romano, cc J. Romie, H. Rong, m D. Rose, E. Rotthoff, S. Rowan, A. Rudiger, 2 P. Russell, K. Ryan, I. Salzman, G. H. Sanders, V. Sannibale, B. Sathyaprakash, P. R. Saulson, R. Savage, A. Sazonov, R. Schilling, 2 K. Schlaufman, V. Schmidt, dd R. Schofield, M. Schrempel, ee B. F. Schutz, 7 P. Schwinberg, S. M. Scott, A. C. Searle, B. Sears, S. Seel, A. S. Sengupta, C. A. Shapiro, ff P. Shawhan, D. H. Shoemaker, Q. Z. Shu, gg A. Sibley, X. Siemens, L. Sievers, h D. Sigg, A. M. Sintes, 33 K. Skeldon, J. R. Smith, M. Smith, M. R. Smith, P. Sneddon, R. Spero, h G. Stapfer, K. A. Strain, D. Strom, A. Stuver, T. Summerscales, M. C. Sumner, P. J. Sutton, y J. Sylvestre, A. Takamori, D. B. Tanner, H. Tariq, I. Taylor, R. Taylor, K. S. Thorne, M. Tibbits, S. Tilav, hh M. Tinto, h K. V. Tokmakov, C. Torres, C. Torrie, 36 S. Traeger, ii G. Traylor, W. Tyler, D. Ugolini, M. Vallisneri, jj M. van Putten, S. Vass, A. Vecchio, C. Vorvick, S. P. Vyachanin, L. Wallace, H. Walther, H. Ward, B. Ware, h K. Watts, D. Webber, A. Weidner, 2 U. Weiland, A. Weinstein, R. Weiss, H. Welling, L. Wen, S. Wen, J. T. Whelan, S. E. Whitcomb, B. F. Whiting, P. A. Willems, P. R. Williams, kk R. Williams, B. Willke, 2 A. Wilson, B. J. Winjum, d W. Winkler, 2 S. Wise, A. G. Wiseman, G. Woan, R. Wooley, J. Worden, I. Yakushin, H. Yamamoto, S. Yoshida, I. Zawischa, ll L. Zhang, N. Zotov, M. Zucker, and J. Zweizig

Journal ArticleDOI
TL;DR: Some interesting results towards the stabilization of the input–output formalism are reported.
Abstract: Reliable and efficient algorithms are needed to model complex mechanical systems such as multiple stage pendulum suspensions. A possible approach is the one based on the input–output formalism. This method allows us to model the system in a modular way. The basic objects (which are the individual stages) are modelled via matrices and then simply joined together through matrix multiplication. It is currently not widely used because it is known to be unstable. Some interesting results towards the stabilization of such algorithm are reported.