Editing Gyroscope (section)

==Variations==

===Gyrostat<!--'Gyrostat' redirects here-->===
[[File:NASM-A19800429000 CU01.jpg|thumb|right|A gyrostat from 1929 made from a bicycle wheel. It was used by [[Robert H. Goddard|Robert Goddard]] to test gyroscopic control of rockets.]]
A '''gyrostat'''<!--boldface per WP:R#PLA--> consists of a massive flywheel concealed in a solid casing.<ref>William Thomson (1875). ''Proc. London Math. Soc.'', vol. 6, pages 190–194.</ref><ref>[[Andrew Gray (physicist)|Andrew Gray]] (1979). ''A Treatise on Gyrostatics and Rotational Motion: Theory and Applications'' (Dover, New York)</ref> Its behaviour on a table, or with various modes of suspension or support, serves to illustrate the curious reversal of the ordinary laws of static equilibrium due to the gyrostatic behaviour of the interior invisible flywheel when rotated rapidly. The first gyrostat was designed by [[Lord Kelvin]] to illustrate the more complicated state of motion of a spinning body when free to wander about on a horizontal plane, like a top spun on the pavement, or a bicycle on the road.<ref>{{EB1911|inline=y|wstitle=Gyroscope and Gyrostat|volume=12|page=769|first=Alfred George|last=Greenhill|author-link=Alfred George Greenhill}} This source has a detailed mathematical discussion of the theory of gyroscopy.</ref> Kelvin<ref>William Thomson, "Popular Lectures and Addresses", London:  MacMillan, 1889, vol. 1.</ref> also made use of gyrostats to develop mechanical theories of the elasticity of matter and of the ether.<ref>Robert Kargon, Peter Achinstein, Baron William Thomson Kelvin: "Kelvin's Baltimore Lectures and Modern Theoretical Physics: Historical and Philosophical Perspectives" [[The MIT Press]], 1987, {{ISBN|978-0-262-11117-1}}</ref> In modern [[continuum mechanics]] there is a variety of these models, based on ideas of Lord Kelvin. They represent a specific type of Cosserat theories (suggested for the first time by [[Eugène Cosserat]] and [[François Cosserat]]), which can be used for description of artificially made smart materials as well as of other complex media. One of them, so-called Kelvin's medium, has the same equations as magnetic insulators near the state of magnetic saturation in the approximation of quasimagnetostatics.<ref>E. Grekova, P. Zhilin (2001). ''Journal of elasticity'', Springer, vol. 64, pages 29–70</ref>

In modern times, the gyrostat concept is used in the design of attitude control systems for orbiting spacecraft and satellites.<ref>Peter C. Hughes (2004). ''Spacecraft Attitude Dynamics'' {{ISBN|0-486-43925-9}}</ref> For instance, the Mir space station had three pairs of internally mounted flywheels known as ''gyrodynes'' or [[control moment gyroscope]]s.<ref>D. M. Harland (1997)  ''The MIR Space Station'' (Wiley); D. M. Harland (2005) ''The Story of Space Station MIR'' (Springer).</ref>

In physics, there are several systems whose dynamical equations resemble the equations of motion of a gyrostat.<ref>C. Tong (2009). ''American Journal of Physics'' vol. 77, pages 526–537</ref> Examples include a solid body with a cavity filled with an inviscid, incompressible, homogeneous liquid,<ref>N.N. Moiseyev and V.V. Rumyantsev (1968). ''Dynamic Stability of Bodies Containing Fluid'' (Springer, New York)</ref> the static equilibrium configuration of a stressed elastic rod in [[elastica theory]],<ref>[[Joseph Larmor]] (1884). ''Proc. London Math. Soc.'' vol. 15, pages 170–184</ref> the polarization dynamics of a light pulse propagating through a nonlinear medium,<ref>M.V. Tratnik and J.E. Sipe (1987). ''Physical Review A'' vol. 35, pages 2965–2975</ref> the [[Lorenz system]] in chaos theory,<ref>A.B. Gluhovsky (1982). ''Soviet Physics Doklady'' vol. 27, pages 823–825</ref> and the motion of an ion in a [[Penning trap]] mass spectrometer.<ref>S. Eliseev et al. (2011). ''Physical Review Letters'' vol. 107, paper 152501</ref>

=== MEMS gyroscope ===
{{main article|Vibrating structure gyroscope}}

A [[microelectromechanical systems]] (MEMS) gyroscope is a miniaturized gyroscope found in electronic devices. It takes the idea of the [[Foucault pendulum]] and uses a vibrating element. This kind of gyroscope was first used in military applications but has since been adopted for increasing commercial use.<ref>{{Cite journal|last1=Passaro|first1=Vittorio M. N.|last2=Cuccovillo|first2=Antonello|last3=Vaiani|first3=Lorenzo|last4=De Carlo|first4=Martino|last5=Campanella|first5=Carlo Edoardo|date=7 October 2017|title=Gyroscope Technology and Applications: A Review in the Industrial Perspective|journal=Sensors (Basel, Switzerland)|volume=17|issue=10|page=2284|doi=10.3390/s17102284|issn=1424-8220|pmc=5677445|pmid=28991175|bibcode=2017Senso..17.2284P|doi-access=free}}</ref>

=== HRG ===

The [[hemispherical resonator gyroscope]] (HRG), also called a wine-glass gyroscope<ref>{{Cite book |last=Grewal |first=Mohinder S. |url=https://www.worldcat.org/oclc/663976587 |title=Global positioning systems, inertial navigation, and integration |date=2007 |publisher=Wiley-Interscience |others=Lawrence R. Weill, Angus P. Andrews |isbn=978-1-61583-471-6 |edition=2nd |location=Hoboken, N.J. |pages=329–331 |oclc=663976587}}</ref> or mushroom gyro, makes use of a thin solid-state hemispherical shell, anchored by a thick stem. This shell is driven to a flexural resonance by electrostatic forces generated by electrodes which are deposited directly onto separate fused-quartz structures that surround the shell. Gyroscopic effect is obtained from the inertial property of the flexural standing waves.<ref>{{Cite journal |last1=Carta |first1=G. |last2=Nieves |first2=M. J. |last3=Jones |first3=I. S. |last4=Movchan |first4=N. V. |last5=Movchan |first5=A. B. |date=2019-10-21 |title=Flexural vibration systems with gyroscopic spinners |journal=Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences |volume=377 |issue=2156 |pages=20190154 |doi=10.1098/rsta.2019.0154 |issn=1471-2962 |pmc=6732376 |pmid=31474205|bibcode=2019RSPTA.37790154C }}</ref>

=== VSG or CVG ===

A [[vibrating structure gyroscope]] (VSG), also called a Coriolis vibratory gyroscope (CVG),<ref>{{cite journal|url=http://www.isprs.org/proceedings/XXXVI/5-C55/www.cirgeo.unipd.it/cirgeo/convegni/mmt2007/proceedings/papers/sternberg_harald.pdf |journal=International Society for Photogrammetry and Remote Sensing Proceedings |year=2007 |title=Qualification Process for MEMS Gyroscopes for the Use in Navigation Systems |author1=H. Sternberg |author2=C. Schwalm |url-status=dead |archive-url=https://web.archive.org/web/20111002084552/http://www.isprs.org/proceedings/XXXVI/5-C55/www.cirgeo.unipd.it/cirgeo/convegni/mmt2007/proceedings/papers/sternberg_harald.pdf |archive-date=2 October 2011 }}</ref> uses a resonator made of different metallic alloys. It takes a position between the low-accuracy, low-cost MEMS gyroscope and the higher-accuracy and higher-cost fiber optic gyroscope. Accuracy parameters are increased by using low-intrinsic damping materials, resonator vacuumization, and digital electronics to reduce temperature dependent drift and instability of control signals.<ref>{{cite journal |url=http://md1.csa.com/partners/viewrecord.php?requester=gs&collection=TRD&recid=A0017841AH&q=coriolis+vibratory+gyroscope+CVG&uid=789572486&setcookie=yes |title=Micromechanical inertial sensor development at Draper Laboratory with recent test results |journal=Symposium Gyro Technology Proceedings |date=14–15 September 1999 |author1=Ash, M E |author2=Trainor, C V |author3=Elliott, R D |author4=Borenstein, J T |author5=Kourepenis, A S |author6=Ward, P A |author7=Weinberg, M S |url-status=dead |archive-url=https://web.archive.org/web/20120823133655/https://md1.csa.com/partners/viewrecord.php?requester=gs&collection=TRD&recid=A0017841AH&q=coriolis+vibratory+gyroscope+CVG&uid=789572486&setcookie=yes |archive-date=23 August 2012}}</ref>

High quality [[Vibrating structure gyroscope#Wine glass resonator|wine-glass resonators]] are used for precise sensors like HRG.<ref>Lynch, D.D.: HRG development at Delco, Litton, and Northrop Grumman. In: Proceedings of Anniversary Workshop on Solid-State Gyroscopy, 19–21 May 2008. Yalta, Ukraine. Kyiv-Kharkiv. ATS of Ukraine, {{ISBN|978-976-0-25248-5}} (2009)</ref>

=== DTG ===
A dynamically tuned gyroscope (DTG) is a rotor suspended by a universal joint with flexure pivots.<ref>{{cite journal
 |url=http://spiedl.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PSISDG003692000001000101000001&idtype=cvips&gifs=yes&ref=no 
 |title=Modeling the dynamically tuned gyroscope in support of high-bandwidth capture loop design 
 |author=David May 
 |editor2-first=Larry A 
 |editor2-last=Stockum 
 |editor1-first=Michael K 
 |editor1-last=Masten 
 |journal=Proc. SPIE 
 |series=Acquisition, Tracking, and Pointing XIII 
 |volume=3692 
 |year=1999 
 |doi=10.1117/12.352852 
 |pages=101–111 
|bibcode=1999SPIE.3692..101M 
 |s2cid=121290096 
 |url-access=subscription 
 }}{{dead link|date=June 2017 |bot=InternetArchiveBot |fix-attempted=yes }}</ref> The flexure spring stiffness is independent of spin rate. However, the dynamic inertia (from the gyroscopic reaction effect) from the gimbal provides negative spring stiffness proportional to the square of the spin speed (Howe and Savet, 1964; Lawrence, 1998). Therefore, at a particular speed, called the tuning speed, the two moments cancel each other, freeing the rotor from torque, a necessary condition for an ideal gyroscope.

===Ring laser gyroscope===
{{Main article|Ring laser gyroscope}}
A [[ring laser gyroscope]] relies on the [[Sagnac effect]] to measure rotation by measuring the shifting interference pattern of a beam split into two separate beams which travel around the ring in opposite directions.

When the [[Boeing 757]]-200 entered service in 1983, it was equipped with the first suitable ring laser gyroscope. This gyroscope took many years to develop, and the experimental models went through many changes before it was deemed ready for production by the engineers and managers of [[Honeywell]] and [[Boeing]]. It was an outcome of the competition with mechanical gyroscopes, which kept improving. The reason Honeywell, of all companies, chose to develop the laser gyro was that they were the only one that didn't have a successful line of mechanical gyroscopes, so they wouldn't be competing against themselves. The first problem they had to solve was that with laser gyros rotations below a certain minimum could not be detected at all, due to a problem called "lock-in", whereby the two beams act like coupled oscillators and pull each other's frequencies toward convergence and therefore zero output. The solution was to shake the gyro rapidly so that it never settled into lock-in. Paradoxically, too regular of a dithering motion produced an accumulation of short periods of lock-in when the device was at rest at the extremities of its shaking motion. This was cured by applying a random [[white noise]] to the vibration. The material of the block was also changed from quartz to a new glass ceramic [[Cer-Vit]], made by [[Owens Corning]], because of helium leaks.<ref>Donald MacKenzie, ''Knowing Machines: Essays in Technical Change'', MIT Press, 1996, Chapter 4: ''From the Luminiferous Ether to the Boeing 757''</ref>

=== Fiber optic gyroscope ===
{{Main article|Fibre optic gyroscope}}
A [[fiber optic gyroscope]] also uses the interference of light to detect mechanical rotation.  The two-halves of the split beam travel in opposite directions in a coil of [[fiber optic]] cable as long as 5&nbsp;km. Like the [[ring laser gyroscope]], it makes use of the [[Sagnac effect]].<ref>Hervé Lefèvre, ''The Fiber-Optic Gyroscope'', 1993, Artech House Optoelectronics Library, 1993, {{ISBN|0-89006-537-3}}</ref>

=== London moment ===
A [[London moment]] gyroscope relies on the quantum-mechanical phenomenon, whereby a spinning [[superconductor]] generates a [[magnetic field]] whose axis lines up exactly with the spin axis of the gyroscopic rotor. A magnetometer determines the orientation of the generated field, which is [[Interpolation|interpolated]] to determine the axis of rotation. Gyroscopes of this type can be extremely accurate and stable. For example, those used in the [[Gravity Probe B]] experiment measured changes in gyroscope spin axis orientation to better than 0.5 [[Minute of arc|milliarcseconds]] (1.4{{e|-7}} degrees, or about {{val|2.4|e=-9|u=radians}}) over a one-year period.<ref>[http://einstein.stanford.edu/content/fact_sheet/GPB_FactSheet-0405.pdf Einstein.stanford.edu] {{webarchive|url=https://web.archive.org/web/20110514044333/http://einstein.stanford.edu/content/fact_sheet/GPB_FactSheet-0405.pdf |date=14 May 2011 }}. "The GP-B instrument is designed 
to measure changes in gyroscope spin axis orientation to better than 0.5 milliarcseconds (1.4x10-7 degrees) over a one-year period"</ref> This is equivalent to an [[angular separation]] the width of a human hair viewed from {{convert|32|km|mi|sp=us}} away.<ref>{{cite web|url=http://history.msfc.nasa.gov/gravity_probe_b/GravityProbeB_20050400.pdf|title=Gravity Probe B – Extraordinary Technologies|url-status=dead|archive-url=https://web.archive.org/web/20100527111732/http://history.msfc.nasa.gov/gravity_probe_b/GravityProbeB_20050400.pdf|archive-date=27 May 2010|access-date=18 January 2011}}</ref>

The GP-B gyro consists of a nearly-perfect spherical [[Moment of inertia#Rotational symmetry|rotating mass]] made of [[fused quartz]], which provides a [[dielectric]] support for a thin layer of [[niobium]] superconducting material. To eliminate friction found in conventional bearings, the rotor assembly is centered by the electric field from six electrodes. After the initial spin-up by a jet of helium which brings the rotor to 4,000 [[Revolutions per minute|RPM]], the polished gyroscope housing is evacuated to an ultra-high vacuum to further reduce drag on the rotor. Provided the suspension electronics remain powered, the extreme [[rotational symmetry]], lack of friction, and low drag will allow the angular momentum of the rotor to keep it spinning for about 15,000 years.<ref>{{cite web|url=http://einstein.stanford.edu/TECH/technology1.html#gyros|title=Gravity Probe B – Extraordinary Technologies|website=Einstein.stanford.edu|access-date=5 November 2017|url-status=dead|archive-url=https://web.archive.org/web/20110514043657/http://einstein.stanford.edu/TECH/technology1.html#gyros|archive-date=14 May 2011}}</ref>

A sensitive [[SQUID#DC SQUID|DC SQUID]] that can discriminate changes as small as one quantum, or about 2 {{e|-15}} [[Weber (unit)|Wb]], is used to monitor the gyroscope. A [[precession]], or tilt, in the orientation of the rotor causes the London moment magnetic field to shift relative to the housing. The moving field passes through a superconducting pickup loop fixed to the housing, inducing a small electric current. The current produces a voltage across a shunt resistance, which is resolved to spherical coordinates by a microprocessor. The system is designed to minimize Lorentz torque on the rotor.<ref>{{cite book|pages=44–45|title=Vortex Electronics and SQUIDs|first1=Takeshi|last1=Kobayashi|first2=Hisao|last2=Hayakawa|first3=Masayoshi|last3=Tonouchi|date=8 December 2003|publisher=Springer |isbn=9783540402312|url=https://books.google.com/books?id=5mPeUu1i5R8C&q=dc+squid+reduce+lorentz+force&pg=PA44|url-status=live|archive-url=https://web.archive.org/web/20150904042759/https://books.google.com/books?id=5mPeUu1i5R8C&pg=PA44&lpg=PA44&dq=dc+squid+reduce+lorentz+force&source=bl&ots=Vgz9jQ-IyI&sig=KN71efttIEUKdd63LWfmhO33p90&hl=en&sa=X&ei=wiuYVfHbK4vSoATv55OgDQ&ved=0CC8Q6AEwBQ#v=onepage&q=dc%20squid%20reduce%20lorentz%20force&f=false|archive-date=4 September 2015}}</ref><ref>{{cite web|url=https://www.researchgate.net/publication/234292394|title=DC electrostatic gyro suspension system for the Gravity Probe B experiment|website=ResearchGate|url-status=live|archive-url=https://web.archive.org/web/20150705144927/http://www.researchgate.net/publication/234292394_DC_electrostatic_gyro_suspension_system_for_the_Gravity_Probe_B_experiment|archive-date=5 July 2015}}</ref>