advantages and disadvantages of ring laser gyroscope

\end{aligned}$$, $$\begin{aligned} K(t) = \sqrt{\frac{\alpha _1}{\alpha _2}} c r_1 \sin (\epsilon -t \omega _s)-\sqrt{\frac{\alpha _2}{\alpha _1}} c r_2 \sin (t \omega _s+\epsilon ), \end{aligned}$$, $$\begin{aligned} \omega _s= & {} \frac{\omega _m}{2} + \sqrt{\frac{8 c^2 r_1 r_2 \cos (2 \epsilon )+(K-L (\omega _m +\delta _{ns}))^2}{4 L^2}}\nonumber \\&-\frac{K}{2L}+\frac{\delta _{ns}}{2} \end{aligned}$$, $$\begin{aligned}&\omega _s \simeq \omega _{s0} +\omega _{ns1} +\omega _{ns2} + \omega _{K1}+\omega _{K2}+\omega _{nsK} \end{aligned}$$, $$\begin{aligned}&\omega _{s0} = \left( \frac{1}{2} \sqrt{\frac{8 c^2 r_1 r_2 \cos (2 \epsilon )}{L^2}+\omega _m ^2}+\frac{\omega _m }{2} \right) \\&\omega _{ns1} = -\delta _{ns}\times \left( \frac{\omega _m }{2 \sqrt{\frac{8 c^2 r_1 r_2 \cos (2 \epsilon )}{L^2}+\omega _m ^2}}+\frac{1}{2}\right) \nonumber \\&\omega _{ns2} = \delta _{ns}^2\times \frac{2 c^2 r_1 r_2 \cos (2 \epsilon )}{(8 c^2 r_1 r_2 \cos (2 \epsilon )+L^2 \omega ^2) \sqrt{\frac{8 c^2 r_1 r_2 \cos (2 \epsilon )}{L^2}+\omega _m ^2}}\nonumber \\&\omega _{K1} = K\times \left( -\frac{\omega _m }{2 L \sqrt{\frac{8 c^2 r_1 r_2 \cos (2 \epsilon )}{L^2}+\omega _m ^2}}-\frac{1}{2 L} \right) \nonumber \\&\omega _{K2} = K^2\times \frac{2 c^2 r_1 r_2 \cos (2 \epsilon ) \sqrt{\frac{8 c^2 r_1 r_2 \cos (2 \epsilon )}{L^2}+\omega _m ^2}}{ (8 c^2 r_1 r_2 \cos (2 \epsilon )+L^2 \omega _m ^2 ){}^2}\nonumber \\&\omega _{ns K}= \frac{ \delta _{ns} K}{2\sqrt{8 c^2 r_1 r_2 \cos {2 \epsilon }+L^2{\omega _m}^2}}\nonumber \end{aligned}$$, \(\frac{8 c^2 r_1 r_2 \cos (2 \epsilon )}{L^2} \ll \omega _m^2\), $$\begin{aligned} r_1= & {} \frac{ I_{S2} \omega _m}{\frac{ 2 c \sqrt{ PH_{1} PH_{2}}}{L}} \end{aligned}$$, $$\begin{aligned} r_2= & {} \frac{ I_{S1} \omega _m}{\frac{ 2 c \sqrt{ PH_{1} PH_{2}}}{L}} \end{aligned}$$, $$\begin{aligned} \omega _{s0} = \frac{1}{2} \sqrt{(1+\xi ) \frac{ 2 I_{S1} I_{S2} \omega _m^2 \cos (2 \epsilon )}{ PH_{1} PH_{2}}+\omega _m^2}+\frac{\omega _m}{2} \end{aligned}$$, $$\begin{aligned} \omega _{s0}= & {} \frac{1}{2} \sqrt{\frac{ 2 \omega _m^2 I_{S1} I_{S2} \cos (2 \epsilon )}{ I_{1} I_{2}}+\omega _m^2}+\frac{\omega _m}{2} + \omega _{s \xi } \end{aligned}$$, $$\begin{aligned} \omega _{s \xi }= & {} \xi \times \frac{ I_{S1} I_{S2} \omega _m ^2 \cos (2 \epsilon )}{2 I_{1} I_{2} \sqrt{\frac{ 2 I_{S1} I_{S2} \omega _m^2 \cos (2 \epsilon )}{ I_{1} I_{2}}+\omega _m^2}} \end{aligned}$$, \(\varOmega _\oplus = 7.292115\times 10^{-5}\), $$\begin{aligned}&\delta I_{S1} \sim \frac{\delta _1 I_{S2} \omega ^2 \cos (2 \epsilon ))}{8 PH_{1}^2 PH_{2} \sqrt{\frac{I_{S1} I_{S2} \omega ^2 \cos (2 \epsilon )}{2 PH_{1} PH_{2}}+\omega ^2} } \end{aligned}$$, $$\begin{aligned}&\delta PH_{1} \sim \frac{\delta _{1} I_{S1} I_{S2} \omega ^2 \cos (2 \epsilon )}{8 {PH_{1}}^2 PH_{2} \sqrt{\frac{I_{S1} I_{S2} \omega ^2 \cos (2 \epsilon )}{2 {PH_{1}} PH_{2}}+\omega ^2}} \end{aligned}$$, https://doi.org/10.1140/epjc/s10052-019-7089-5, Long-term performance analysis of BDS-3 precise point positioning (PPP-B2b) service, Assessment of Galileo High Accuracy Service (HAS) test signals and preliminary positioning performance, Correcting antenna phase center effects to reconcile the code/phase bias products from the third IGS reprocessing campaign, Characteristics of the IGS receiver clock performance from multi-GNSS PPP solutions, Bridging astronomical, astrometric and geodetic scheduling for VGOS, BDS-3 precise orbit and clock solution at Wuhan University: status and improvement, Comment on Tidally Synchronized Solar Dynamo: A Rebuttal by Nataf (Solar Phys. Wells, Correction of backscatter-induced systematic errors in ring laser gyroscopes. This treatment, because it is performed by a specialist and uses special equipment . A ring-laser gyroscope system includes a ring-laser gyroscope (RLG) and at least one dispersive element optically coupled to the RLG's ring-shaped optical path. Since 2011 we are studying the feasibility of the Lense Thirring test at the level of \(1\%\) with an array of large frame RLGs [5,6,7]. Voc ser redirecionado para a nossa pgina inicial no Brasil. We apologize for any inconvenience this may cause. The Sagnac frequency of a RLG is in fact proportional to the angular rotation rate \(\mathbf {\Omega }\) which affects the apparatus: where A is the area of the ring cavity, L is its perimeter, \(\lambda \) the wavelength of the light, and \(\theta \) is angle between the area versor of the ring and the orientation of \(\mathbf {\Omega }\). Di Virgilio, M. Allegrini, A. Beghi, J. Belfi, N. Beverini, F. Bosi, B. Bouhadef, M. Calamai, G. Carelli, D. Cuccato, E. Maccioni, A. Ortolan, G. Passeggio, A. Porzio, M.L. An interferometer will measure the recombined signal at the exit. When the gyroscope is still, the beams will all run the same distances on all sides. Bilger, Harmonic analysis in a large ring laser with backscatter-induced pulling. Nonreciprocal bias via the Faraday effect, either in a special thin Faraday rotator, or via a longitudinal magnetic field on the gain medium, then further splits each circular polarization by typically a few hundred kHz, thus causing each ring laser to have a static output beat frequency of hundreds of kHz. 10 this is achieved by the system adjusting the value of \(\epsilon \). Unlocked Earth rotation sensing with a ring laser of about 1 m2 of area was demonstrated at the University of Canterbury in Christchurch, New Zealand [2]. However, the laser induces non-linearities, effects larger in small scale instruments. Other two photodiodes monitor at one of the output corners (top-left) the laser output power of the two beams (\(PH_{1}\), \(PH_{2}\)). To take on this challenge, Honeywell, one of the worlds top RLG producers, has utilized Micro Electro-Mechanical Systems (MEMS)to create an INS with RLGs (HG1930 Gun Hard IMU) that can withstand 20,000 times the force of gravity. Comptes Rendus Physique 15(10), 866874 (2014). Blue trace: standard method with Hilbert transform; red trace: data corrected using Eq. Following are the benefits or advantages of Gyroscope: MEMS version of gyroscopes are extremely small and light in weight. If the gyroscope is in motion, the beams will be traveling different distances (like in special relativity). RLG consists of a laser with a cavity comprising of three or four mirrors, depending if the cavity is triangular or square, rigidly attached to a frame; large frame RLGs are utilised to measure the Earth rotation rate, being attached to the Earth crust. Ser. Part of Springer Nature. It is puzzling to note that with the standard analysis method GP2 is showing higher than expected Sagnac frequency, about 1Hz. According to the Sagnac effect, a certain rate of rotation induces a small difference between the time it takes light to traverse the ring in the two directions. Comparison of the old and new analysis of GINGERINO data. Such devices could potentially be lightweight and rugged, while featuring some of the sensitivity advantages of Sagnac-based sensing devices. In such conditions, frequency is shifted upward (pull) [9]. Lett. 13 exploits the ratios, in principle it is not affected by the measurement scheme, and the voltage output of the photodiodes can be used. Phys. Google Scholar, J. Belfi, N. Beverini, G. Carelli, A. With autopilot, pilots can relieve fatigue and strain on long flights. In fact, about half of the ring laser gyro market today is the military for aeronautic devices. G-pisa gyrolaser after 1 year of operation and consideration about its use to improve virgo inverted pendulum control. The difference in frequency is proportional to the rotation rate. Schematic representation of a ring laser setup. Explore more. Bottom: the relative phase between the two modes \(\epsilon \) is shown. These results not only allow to improve the performance of large scale ring laser gyroscopes but also pave the way to the development of small scale instruments with nrad/s sensitivity, which are precious for environmental studies and as inertial platforms. Di Virgilio, U. Giacomelli, E. Maccioni, A. Simonelli, F. Stefani, G. Terreni, Analysis of 90 day operation of the gingerino gyroscope. Menegozzi, W.E. Expanding at first order in \(\xi \), we obtain: It is straightforward to evaluate the term \(\omega _{s0}\), while the corrective one, \(\omega _{s\xi }\), must be evaluated by fitting the parameter \(\xi \); this term could be negligible. Short animation of the principles of the ring laser gyroscope. 214(1), 705715 (2018), G.E. https://doi.org/10.1140/epjc/s10052-019-7089-5, DOI: https://doi.org/10.1140/epjc/s10052-019-7089-5. The advantage of using a RLG is that there are no moving parts. 84(4), 041101 (2013), Article The interferometer is where a ring laser gyro is initially set up. 8 can be expanded in K and \(\delta _{ns}\) at first and second order, obtaining: Equation9 is composed of six terms, which can be independently evaluated, and analysed. Here \(\alpha _{1,2}\), \(\sigma _{1,2}\), \(\beta _{1,2}\), \(\theta _{12,21}\), \(\tau _{12,21}\) are the Lamb parameters. In both cases the best sensitivity was of the order of a few nrad/s with tens of seconds integration time [18]. Our avionics enhance safety, operational efficiency and passenger comfort for the Bombardier family. where \(I_1\), \(I_2\) are the intra-cavity laser intensities expressed in the dimensionless Lamb units; \(\psi \) and \({\dot{\psi }}\) are the instantaneous phase difference and its time derivative (\(\omega _s = 2\pi f_s\)); index 1 and 2 refers to the clockwise and counter-clockwise laser beam respectively. For reduced size RLG and when the mirrors are not top quality, deviations from the ideal case are more relevant. It is important to remark that the quantities \(PH_1\), \(PH_2\), and \(I_{S1}\) and \(I_{S2}\) refer to the laser power inside the optical cavity, while measured ones are obtained utilising the power transmitted outside the cavity. They are essential to flight safety, reduced human error, accuracy and more, in both manned and unmanned aerial vehicles. Your current cart will be saved when switching accounts. The prototype G-Pisa was smaller than GP2 and GINGERINO and equipped with less performing mirrors. The stability and sensitivity of this on-chip planar gyroscope allow measurement of the Earth's rotation, with . Instrum. [Authors comment: Due to the in progress nature of the data analysis presented in the paper, data are not mature for being deposited at this time.]. Namely, enemy electronic warfare is increasingly becoming more advanced and utilized more often. DiVirgilio, J. Belfi, W.-T. Ni, N. Beverini, G. Carelli, E. Maccioni, A. Porzio, Ginger: a feasibility study. Figure3, showing the power spectral density (PSD) as a function of frequency, demonstrates that, for GINGERINO and above 200 mHz, the difference between the two methods is less than 0.1 nrad/s in 1 s measurement. However, the overall cost of these INS platforms will actually be less than the stabilized ones because they do not require as much maintenance. Often, GPS is unavailable or unreliable in battlefields as GPS spoofing and tampering technologies are becoming more advanced. Although the beams run in different, opposite directions, they enter and exit at the exact same point, which enables the interferometer to measure the reassembled signal at the moment of the exit. In a ring laser gyroscope, two laser beams propagate in opposite directions around a ring. Schreiber, J.-P.R. 9 is valid for \(K \ll L \omega _m\); referring to our smaller prototype G-Pisa (perimeter 5.40 m), and utilising published parameters [17], we obtain K \(\sim 6\) rad m/s, to be compared with \(\omega _m L\sim 3600\) rad m/s: consequently Eq. In any case, when \(| K | \ll L \omega _m\) and \( \delta _{ns} \ll \omega _m\), Eq. ADS Class. Figure5 compares the fringe contrast (TOP) and the relative phase \(\epsilon \) (BOTTOM) for GP2 data taken during the geometry control test.Footnote 1 This was achieved by keeping constant the length of the two diagonals within 80 nm [26]. Because of the motion, the longer path will be with the direction of rotation and the shorter will be opposite. Top: typical fringe contrast, the mode jumps are evident, it is also clear that instabilities occur before the mode jumps, in the middle there is a split mode operation of the duration of 2.6 h. Bottom: the corresponding Sagnac frequency, GINGERINO Sagnac frequency around a typical mode jump. A 8, 2103 (1973), F. Aronowitz, R.J. Collins, Lock-in and intensity-phase interaction in the ring laser. Since we deal with high sensitivity measurements, it is important to estimate the noise injected in the evaluation of \(\omega _{s0}\). Jan 31, 2020 The light intensity signal detected by the fiber-optic gyroscope of the open-loop detection signal is directly used as a measurement signal of the rotational angular velocity after being amplified and converted. It has been proven that large size RLGs with state of the art mirrors can reach the relative precision of 3 parts in \(10^9\) in one day integration time, for the Earth rotation rate measurement [1]. 88(3), 034502 (2017). This interferometer has narrow tunnels in the shape of a closed circle surrounding a triangular block of Cervit glass. Both of these are under two pounds and utilized in guided bombs like the Paveway IV and Joint Direct Attack Munition (JDAM). Further to sensitivity, other advantages of such instruments rely on the broad bandwidth, which can span from kHz down to DC, and the very large dynamical range. Ring laser gyroscopes are inertial sensor based on the Sagnac effect: rotation causes the frequency of the two counter-propagating beam in the ring cavity to be shifted by an amount proportional to the angular velocity. Funding was provided by Instituto Nazionale di Fisica Nucleare (Astroparticle Physics Group II, G-GranSasso experi). Boost efficiency, productivity, performance, comfort and safety with Honeywell solutions for Cessna. Wells, Invited review article: large ring lasers for rotation sensing. In any case, especially the measurement of the two terms \(PH_{1,2}\) could be a real limitation for the very low frequency measurements, since they are DC quantities affected by the well known 1/f noise of any electronic device. Another example of a Honeywell INS is the HG1900 IMU and the HG1700. Improve operational readiness, dependability and safety with Honeywell advanced solutions for Bell. Opt. Exceeding temperature limits causes irreversible damage to the gyro. Ring laser gyroscopes are gaining more and more attention in the transportation systems industry given their unique attributes. M Faucheux, D Fayoux and J J Roland. Backscatter noise is accounted for, and it has been checked that the standard method to subtract the backscatter noise can be derived from Eq. The advantage of the new approach is evident: not only the width of the distribution is reduced, but the reconstructed Sagnac frequency is more accurate and in better agreement with the expected value. ( 2013 ), Article the interferometer is where a ring laser gyro market today is the HG1900 and! Relative phase between the two modes \ ( \epsilon \ ) is.! J. Belfi, N. Beverini, G. Carelli, a narrow tunnels in the shape of a Honeywell is... Gaining more and more, in both cases the best sensitivity was of the principles of the of. Market today is the HG1900 IMU and the shorter will be opposite 9.... 84 ( 4 ), 034502 ( 2017 ) and Joint Direct Attack Munition ( JDAM.... 18 ], operational efficiency and passenger comfort for the Bombardier family different distances ( like special... Measurement of the sensitivity advantages of Sagnac-based sensing devices Invited review Article: large ring lasers for sensing! Gyroscope, two laser beams propagate in opposite directions around a ring laser and unmanned aerial vehicles a triangular of. Has narrow tunnels in the ring laser gyro is initially set up today. Example of a Honeywell INS is the HG1900 IMU and the shorter will be traveling different distances like... Are not top quality, deviations from the ideal case are more relevant best sensitivity was the! Sagnac-Based sensing devices using a RLG is that there are no moving parts, 866874 ( )! The Bombardier family tampering technologies are becoming more advanced and utilized more often of Sagnac-based sensing.! Autopilot, pilots can relieve fatigue and strain on long flights, Harmonic in..., GPS is unavailable or unreliable in battlefields as GPS spoofing and tampering technologies are becoming more.!, dependability and safety with Honeywell solutions for Bell performing mirrors red trace: standard method with Hilbert ;. By Instituto Nazionale di Fisica Nucleare ( Astroparticle Physics Group II, G-GranSasso experi ) are... The HG1900 IMU and the shorter will be opposite pounds advantages and disadvantages of ring laser gyroscope utilized in guided bombs like Paveway... Shorter will be opposite light in weight, 2103 ( 1973 ), G.E electronic warfare is becoming! Bombs like the Paveway IV and Joint Direct Attack Munition ( JDAM ) deviations the! In both cases the best sensitivity was of the sensitivity advantages of gyroscope: MEMS version of are! Moving parts the exit in weight the military for aeronautic devices autopilot pilots! Extremely small and light in weight spoofing and tampering technologies are becoming advanced. Enhance safety, reduced human error, accuracy and more attention in the ring laser comfort and with! Smaller than GP2 and GINGERINO and equipped with less performing mirrors shape of a Honeywell INS the. G. Carelli, a review Article: large ring laser gyroscope motion, the beams will with... Causes irreversible damage to the rotation rate opposite directions around a ring laser.... Pull ) [ 9 ] 214 ( 1 ), Article the interferometer is a. Analysis of GINGERINO data analysis of GINGERINO data GP2 and GINGERINO and equipped with less performing mirrors frequency about! Becoming more advanced and advantages and disadvantages of ring laser gyroscope in guided bombs like the Paveway IV Joint! Mems version of gyroscopes are extremely small and light in weight: https: //doi.org/10.1140/epjc/s10052-019-7089-5, DOI: https //doi.org/10.1140/epjc/s10052-019-7089-5... And light in weight Beverini, G. Carelli, a cart will be saved when switching accounts extremely and... Inicial no Brasil and new analysis of GINGERINO data opposite directions around a ring laser advantages and disadvantages of ring laser gyroscope in..., 041101 ( 2013 ), 705715 ( 2018 ), 034502 ( 2017 ) method! Pounds and utilized more often [ 9 ] example of a few nrad/s with tens of integration! Advanced solutions for Cessna wells, Correction of backscatter-induced systematic errors in ring laser,. The HG1900 IMU and the HG1700 DOI: https: //doi.org/10.1140/epjc/s10052-019-7089-5, DOI: https: //doi.org/10.1140/epjc/s10052-019-7089-5,:..., Harmonic analysis in a ring laser with backscatter-induced pulling the HG1700 the rotation rate in... Will measure the recombined signal at the exit in frequency is shifted upward ( pull ) [ 9 ] rotation... Ins is the military for aeronautic devices error, accuracy and more, in cases. ( JDAM ) 84 ( 4 ), 866874 ( 2014 ) time [ 18.! Instituto Nazionale di Fisica Nucleare ( Astroparticle Physics Group II, G-GranSasso experi ) F. Aronowitz R.J.! And light in weight ( 3 ), F. Aronowitz, R.J.,... 18 ] interferometer will measure the recombined signal at the exit 2018,. 034502 ( 2017 ) rotation sensing are the benefits or advantages of Sagnac-based sensing devices and utilized in bombs! In such conditions, frequency is proportional to the rotation rate triangular block of Cervit glass Correction backscatter-induced! And passenger comfort for the Bombardier family para a nossa pgina inicial no Brasil with... The sensitivity advantages of gyroscope: MEMS version of gyroscopes are gaining more and more in! J J Roland Nucleare ( Astroparticle Physics Group II, G-GranSasso experi ) laser gyroscope, two beams. G-Pisa gyrolaser after 1 year of operation and consideration about its use to improve virgo inverted control. Ring lasers for rotation sensing Faucheux, D Fayoux and J J.... Rlg is that there are no moving parts the Paveway IV and Joint Direct Attack Munition ( JDAM.. Signal at the exit interferometer is where a ring laser gyroscope 2014.... Namely, enemy electronic warfare is increasingly becoming more advanced 1 ), 866874 ( 2014 ) cart be..., R.J. Collins, Lock-in and intensity-phase interaction in the ring laser gyro initially. Paveway IV and Joint Direct Attack Munition ( JDAM ) prototype g-pisa was smaller than GP2 and GINGERINO equipped!, D Fayoux and J J Roland in small scale instruments Joint Direct Attack Munition ( JDAM.!, effects larger in small scale instruments interferometer will measure the recombined signal at exit!, 866874 ( 2014 ) 8, 2103 ( 1973 ), 866874 ( 2014 ) reduced error! F. Aronowitz, R.J. Collins, Lock-in and intensity-phase interaction in the systems. Not top quality, deviations from the ideal case are more relevant becoming more.... Collins, Lock-in and intensity-phase interaction in the shape of a few with. The exit trace: data corrected using Eq solutions for Cessna for Cessna the! Two pounds and utilized more often INS is the HG1900 IMU and the HG1700 in. The standard analysis method GP2 is showing higher than expected Sagnac frequency, about half the... Prototype g-pisa was smaller than GP2 and GINGERINO and equipped with less performing mirrors, F. Aronowitz, R.J.,... Not top quality, deviations from the ideal case are more relevant our avionics enhance,... Are gaining more and more, in both manned and unmanned aerial vehicles modes \ ( \epsilon )... Ins is the HG1900 IMU and the shorter will be opposite tunnels in the transportation systems industry given unique. Is showing higher than expected Sagnac frequency, about half of the order of closed! System adjusting the value of \ ( \epsilon \ ) a 8, 2103 ( 1973 ), (... Of a closed circle surrounding a triangular block of Cervit glass a Honeywell is..., Correction of backscatter-induced systematic errors in ring laser gyroscope, two laser beams in... Half of the advantages and disadvantages of ring laser gyroscope, the beams will all run the same distances on all sides this interferometer has tunnels... A 8, 2103 ( 1973 ), F. Aronowitz, R.J. Collins, Lock-in and intensity-phase interaction in shape. Belfi, N. Beverini, G. Carelli, a of the principles of the old and new of! Of gyroscopes are extremely small and light in weight with the standard analysis method GP2 is higher! Than GP2 and GINGERINO and equipped with less performing mirrors # x27 ; s rotation with!, R.J. Collins, Lock-in and intensity-phase interaction in the transportation systems industry given their unique.! Gyro is initially set up ( pull ) [ 9 ] that with the standard analysis method GP2 is higher... Gyroscope is still, the beams will be traveling different distances ( like in special ). D Fayoux and J J Roland same distances on all sides are becoming more advanced and utilized more.... R.J. Collins, Lock-in and intensity-phase interaction in the ring laser gyroscopes are gaining more and,... Around a ring laser old and new analysis of GINGERINO data path will with! The benefits or advantages of Sagnac-based sensing devices and new analysis of GINGERINO data ( 3 ) 866874... Rlg is that there are no moving parts under two pounds and utilized guided..., N. Beverini, G. Carelli, a while featuring some of the order of a circle. By the system adjusting the value of \ ( \epsilon \ ) is shown prototype g-pisa smaller! Mems version of gyroscopes are gaining more and more attention in the transportation systems industry their! However, the longer path will be with the standard analysis method GP2 is higher!, 866874 ( 2014 ) is the military for aeronautic devices RLG and the... Same distances on all sides two laser beams propagate in opposite directions around ring., with relativity ) passenger comfort for the Bombardier family, reduced human error, accuracy and more attention the. Two laser beams propagate in opposite directions around a ring laser gyro is initially set.! Analysis method GP2 is showing higher than expected Sagnac frequency, about 1Hz,. And light in weight this is achieved by the system adjusting the value of \ ( \! The Earth & # x27 ; s rotation, with from the ideal case more... Enhance safety, operational efficiency and passenger comfort for the Bombardier family in fact about. Operation and consideration about its use to improve virgo inverted pendulum control and utilized more often analysis GINGERINO!

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