Virtual reality - Wikipedia
Virtual reality (VR) is a simulated experience that employs 3D near-eye displays and pose tracking to give the user an immersive feel of a virtual world.
gyroscopes
Modern virtual reality headset displays are based on technology developed for smartphones including: <anchor>gyroscopes</anchor> and motion sensors for tracking head, body, and hand positions; small HD screens for stereoscopic displays; and small, lightweight and fast computer processors. These components led to relative affordability for independent VR developers, and led to the 2012 Oculus Rift Kickstarter offering the first independently developed VR headset.[54]
Gyroscope - Wikipedia
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## Contents

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- (Top)

- [1Description and diagram](#Description_and_diagram)
- [2History](#History)Toggle History subsection  - [2.1Early similar devices](#Early_similar_devices)
  - [2.2Foucault's gyroscope](#Foucault's_gyroscope)
  - [2.3Commercialization](#Commercialization)
- [3Gyroscopic principles](#Gyroscopic_principles)Toggle Gyroscopic principles subsection  - [3.1Rigidity in space](#Rigidity_in_space)
  - [3.2Precession](#Precession)
- [4Contemporary uses](#Contemporary_uses)Toggle Contemporary uses subsection  - [4.1Steadicam](#Steadicam)
  - [4.2Heading indicator](#Heading_indicator)
  - [4.3Gyrocompass](#Gyrocompass)
  - [4.4Accelerometer](#Accelerometer)
- [5Variations](#Variations)Toggle Variations subsection  - [5.1Gyrostat](#Gyrostat)
  - [5.2MEMS gyroscope](#MEMS_gyroscope)
  - [5.3HRG](#HRG)
  - [5.4VSG or CVG](#VSG_or_CVG)
  - [5.5DTG](#DTG)
  - [5.6Ring laser gyroscope](#Ring_laser_gyroscope)
  - [5.7Fiber optic gyroscope](#Fiber_optic_gyroscope)
  - [5.8London moment](#London_moment)
- [6Other examples](#Other_examples)Toggle Other examples subsection  - [6.1Helicopters](#Helicopters)
  - [6.2Gyro X](#Gyro_X)
- [7Consumer electronics](#Consumer_electronics)
- [8See also](#See_also)
- [9Notes](#Notes)
- [10References](#References)
- [11Further reading](#Further_reading)
- [12External links](#External_links)

Toggle the table of contents

# Gyroscope

75 languages

- [Afrikaans](https://af.wikipedia.org/wiki/Giroskoop "Giroskoop – Afrikaans")
- [العربية](https://ar.wikipedia.org/wiki/%D8%AF%D9%88%D8%A7%D9%85 "دوام – Arabic")
- [Asturianu](https://ast.wikipedia.org/wiki/Xiroscopiu "Xiroscopiu – Asturian")
- [Azərbaycanca](https://az.wikipedia.org/wiki/Giroskop "Giroskop – Azerbaijani")
- [বাংলা](https://bn.wikipedia.org/wiki/%E0%A6%98%E0%A7%82%E0%A6%B0%E0%A7%8D%E0%A6%A3%E0%A6%A8%E0%A6%AC%E0%A7%80%E0%A6%95%E0%A7%8D%E0%A6%B7%E0%A6%95 "ঘূর্ণনবীক্ষক – Bangla")
- [Беларуская](https://be.wikipedia.org/wiki/%D0%93%D1%96%D1%80%D0%B0%D1%81%D0%BA%D0%BE%D0%BF "Гіраскоп – Belarusian")
- [Български](https://bg.wikipedia.org/wiki/%D0%96%D0%B8%D1%80%D0%BE%D1%81%D0%BA%D0%BE%D0%BF "Жироскоп – Bulgarian")
- [Bosanski](https://bs.wikipedia.org/wiki/%C5%BDiroskop "Žiroskop – Bosnian")
- [Català](https://ca.wikipedia.org/wiki/Giroscopi "Giroscopi – Catalan")
- [Чӑвашла](https://cv.wikipedia.org/wiki/%D0%93%D0%B8%D1%80%D0%BE%D1%81%D0%BA%D0%BE%D0%BF "Гироскоп – Chuvash")
- [Čeština](https://cs.wikipedia.org/wiki/Gyroskop "Gyroskop – Czech")
- [Dansk](https://da.wikipedia.org/wiki/Gyroskop "Gyroskop – Danish")
- [Deutsch](https://de.wikipedia.org/wiki/Kreiselinstrument "Kreiselinstrument – German")
- [Eesti](https://et.wikipedia.org/wiki/G%C3%BCroskoop "Güroskoop – Estonian")
- [Ελληνικά](https://el.wikipedia.org/wiki/%CE%93%CF%85%CF%81%CE%BF%CF%83%CE%BA%CF%8C%CF%80%CE%B9%CE%BF "Γυροσκόπιο – Greek")
- [Español](https://es.wikipedia.org/wiki/Gir%C3%B3scopo "Giróscopo – Spanish")
- [Esperanto](https://eo.wikipedia.org/wiki/Giroskopo "Giroskopo – Esperanto")
- [Euskara](https://eu.wikipedia.org/wiki/Giroskopio "Giroskopio – Basque")
- [فارسی](https://fa.wikipedia.org/wiki/%DA%98%DB%8C%D8%B1%D9%88%D8%B3%DA%A9%D9%88%D9%BE "ژیروسکوپ – Persian")
- [Français](https://fr.wikipedia.org/wiki/Gyroscope "Gyroscope – French")
- [Gaeilge](https://ga.wikipedia.org/wiki/G%C3%ADreasc%C3%B3p "Gíreascóp – Irish")
- [Galego](https://gl.wikipedia.org/wiki/Xiroscopio "Xiroscopio – Galician")
- [贛語](https://gan.wikipedia.org/wiki/%E9%99%80%E8%9E%BA%E5%84%80 "陀螺儀 – Gan")
- [한국어](https://ko.wikipedia.org/wiki/%EC%9E%90%EC%9D%B4%EB%A1%9C%EC%8A%A4%EC%BD%94%ED%94%84 "자이로스코프 – Korean")
- [Հայերեն](https://hy.wikipedia.org/wiki/%D4%B3%D5%AB%D6%80%D5%B8%D5%BD%D5%AF%D5%B8%D5%BA "Գիրոսկոպ – Armenian")
- [हिन्दी](https://hi.wikipedia.org/wiki/%E0%A4%98%E0%A5%82%E0%A4%B0%E0%A5%8D%E0%A4%A3%E0%A4%BE%E0%A4%95%E0%A5%8D%E0%A4%B7%E0%A4%A6%E0%A4%B0%E0%A5%8D%E0%A4%B6%E0%A5%80 "घूर्णाक्षदर्शी – Hindi")
- [Hrvatski](https://hr.wikipedia.org/wiki/%C5%BDiroskop "Žiroskop – Croatian")
- [Ido](https://io.wikipedia.org/wiki/Giroskopo "Giroskopo – Ido")
- [Bahasa Indonesia](https://id.wikipedia.org/wiki/Giroskop "Giroskop – Indonesian")
- [Íslenska](https://is.wikipedia.org/wiki/Sn%C3%BA%C3%B0ur "Snúður – Icelandic")
- [Italiano](https://it.wikipedia.org/wiki/Giroscopio "Giroscopio – Italian")
- [עברית](https://he.wikipedia.org/wiki/%D7%92%D7%99%D7%A8%D7%95%D7%A1%D7%A7%D7%95%D7%A4 "גירוסקופ – Hebrew")
- [Қазақша](https://kk.wikipedia.org/wiki/%D0%93%D0%B8%D1%80%D0%BE%D1%81%D0%BA%D0%BE%D0%BF "Гироскоп – Kazakh")
- [Kriyòl gwiyannen](https://gcr.wikipedia.org/wiki/Jirosk%C3%B2p "Jiroskòp – Guianan Creole")
- [Кыргызча](https://ky.wikipedia.org/wiki/%D0%93%D0%B8%D1%80%D0%BE%D1%81%D0%BA%D0%BE%D0%BF "Гироскоп – Kyrgyz")
- [Latina](https://la.wikipedia.org/wiki/Gyroscopium "Gyroscopium – Latin")
- [Latviešu](https://lv.wikipedia.org/wiki/%C5%BDiroskops "Žiroskops – Latvian")
- [Lëtzebuergesch](https://lb.wikipedia.org/wiki/Gyroskop "Gyroskop – Luxembourgish")
- [Lietuvių](https://lt.wikipedia.org/wiki/Giroskopas "Giroskopas – Lithuanian")
- [Magyar](https://hu.wikipedia.org/wiki/Giroszk%C3%B3p "Giroszkóp – Hungarian")
- [മലയാളം](https://ml.wikipedia.org/wiki/%E0%B4%9C%E0%B5%88%E0%B4%B1%E0%B5%8B%E0%B4%B8%E0%B5%8D%E0%B4%95%E0%B5%8B%E0%B4%AA%E0%B5%8D%E0%B4%AA%E0%B5%8D "ജൈറോസ്കോപ്പ് – Malayalam")
- [Bahasa Melayu](https://ms.wikipedia.org/wiki/Giroskop "Giroskop – Malay")
- [Mirandés](https://mwl.wikipedia.org/wiki/Girosc%C3%B3pio "Giroscópio – Mirandese")
- [မြန်မာဘာသာ](https://my.wikipedia.org/wiki/%E1%80%82%E1%80%BB%E1%80%AD%E1%80%AF%E1%80%84%E1%80%BA%E1%80%9B%E1%80%AD%E1%80%AF%E1%80%85%E1%80%80%E1%80%AF%E1%80%95%E1%80%BA "ဂျိုင်ရိုစကုပ် – Burmese")
- [Nederlands](https://nl.wikipedia.org/wiki/Gyroscoop "Gyroscoop – Dutch")
- [日本語](https://ja.wikipedia.org/wiki/%E3%82%B8%E3%83%A3%E3%82%A4%E3%83%AD%E3%82%B9%E3%82%B3%E3%83%BC%E3%83%97 "ジャイロスコープ – Japanese")
- [Norsk bokmål](https://no.wikipedia.org/wiki/Gyroskop "Gyroskop – Norwegian Bokmål")
- [Norsk nynorsk](https://nn.wikipedia.org/wiki/Gyroskop "Gyroskop – Norwegian Nynorsk")
- [ଓଡ଼ିଆ](https://or.wikipedia.org/wiki/%E0%AC%97%E0%AC%BE%E0%AC%87%E0%AC%B0%E0%AD%8B%E0%AC%B8%E0%AD%8D%E0%AC%95%E0%AD%8B%E0%AC%AA "ଗାଇରୋସ୍କୋପ – Odia")
- [Oʻzbekcha / ўзбекча](https://uz.wikipedia.org/wiki/Giroskop "Giroskop – Uzbek")
- [پښتو](https://ps.wikipedia.org/wiki/%D8%AC%D9%8A%D8%B1%D9%88%D8%B3%D9%83%D9%88%D9%BE "جيروسكوپ – Pashto")
- [Patois](https://jam.wikipedia.org/wiki/Jairoskuop "Jairoskuop – Jamaican Creole English")
- [Piemontèis](https://pms.wikipedia.org/wiki/Girosc%C3%B2pi "Giroscòpi – Piedmontese")
- [Polski](https://pl.wikipedia.org/wiki/%C5%BByroskop "Żyroskop – Polish")
- [Português](https://pt.wikipedia.org/wiki/Girosc%C3%B3pio "Giroscópio – Portuguese")
- [Română](https://ro.wikipedia.org/wiki/Giroscop "Giroscop – Romanian")
- [Русский](https://ru.wikipedia.org/wiki/%D0%93%D0%B8%D1%80%D0%BE%D1%81%D0%BA%D0%BE%D0%BF "Гироскоп – Russian")
- [Simple English](https://simple.wikipedia.org/wiki/Gyroscope "Gyroscope – Simple English")
- [Slovenčina](https://sk.wikipedia.org/wiki/Gyroskop "Gyroskop – Slovak")
- [Slovenščina](https://sl.wikipedia.org/wiki/%C5%BDiroskop "Žiroskop – Slovenian")
- [کوردی](https://ckb.wikipedia.org/wiki/%D8%AC%D8%A7%DB%8C%D8%B1%DB%86%D8%B3%DA%A9%DB%86%D9%BE "جایرۆسکۆپ – Central Kurdish")
- [Српски / srpski](https://sr.wikipedia.org/wiki/%D0%96%D0%B8%D1%80%D0%BE%D1%81%D0%BA%D0%BE%D0%BF "Жироскоп – Serbian")
- [Srpskohrvatski / српскохрватски](https://sh.wikipedia.org/wiki/%C5%BDiroskop "Žiroskop – Serbo-Croatian")
- [Suomi](https://fi.wikipedia.org/wiki/Gyroskooppi "Gyroskooppi – Finnish")
- [Svenska](https://sv.wikipedia.org/wiki/Gyroskop "Gyroskop – Swedish")
- [தமிழ்](https://ta.wikipedia.org/wiki/%E0%AE%9A%E0%AF%81%E0%AE%B4%E0%AE%B2%E0%AF%8D_%E0%AE%95%E0%AE%BE%E0%AE%9F%E0%AF%8D%E0%AE%9F%E0%AE%BF "சுழல் காட்டி – Tamil")
- [ไทย](https://th.wikipedia.org/wiki/%E0%B9%84%E0%B8%88%E0%B9%82%E0%B8%A3%E0%B8%AA%E0%B9%82%E0%B8%81%E0%B8%9B "ไจโรสโกป – Thai")
- [Тоҷикӣ](https://tg.wikipedia.org/wiki/%D0%A7%D0%B0%D1%80%D1%85%D0%B8%D1%88%D0%BD%D0%B0%D0%BC%D0%BE "Чархишнамо – Tajik")
- [Türkçe](https://tr.wikipedia.org/wiki/Jiroskop "Jiroskop – Turkish")
- [Українська](https://uk.wikipedia.org/wiki/%D0%93%D1%96%D1%80%D0%BE%D1%81%D0%BA%D0%BE%D0%BF "Гіроскоп – Ukrainian")
- [اردو](https://ur.wikipedia.org/wiki/%DA%AF%D8%B1%D8%AF%D8%B4_%D9%86%D9%85%D8%A7 "گردش نما – Urdu")
- [Tiếng Việt](https://vi.wikipedia.org/wiki/Con_quay_h%E1%BB%93i_chuy%E1%BB%83n "Con quay hồi chuyển – Vietnamese")
- [吴语](https://wuu.wikipedia.org/wiki/%E9%99%80%E8%9E%BA%E4%BB%AA "陀螺仪 – Wu")
- [粵語](https://zh-yue.wikipedia.org/wiki/%E9%99%80%E8%9E%BA%E5%84%80 "陀螺儀 – Cantonese")
- [中文](https://zh.wikipedia.org/wiki/%E9%99%80%E8%9E%BA%E5%84%80 "陀螺儀 – Chinese")

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From Wikipedia, the free encyclopedia

Device for measuring or maintaining the orientation and angular velocity

For other uses and non-rotary gyroscopes, see [Gyroscope (disambiguation)](/wiki/Gyroscope_(disambiguation) "Gyroscope (disambiguation)").

[![](//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/3D_Gyroscope.png/250px-3D_Gyroscope.png)](/wiki/File:3D_Gyroscope.png) A gyroscope[![](//upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Gyroscope_operation.gif/220px-Gyroscope_operation.gif)](/wiki/File:Gyroscope_operation.gif) A gyroscope in operation, showing the freedom of rotation in all three axes. The rotor will maintain its spin axis direction regardless of the orientation of the outer frame.

A **gyroscope** (from [Ancient Greek](/wiki/Ancient_Greek "Ancient Greek") γῦρος _gŷros_, "round" and σκοπέω _skopéō_, "to look") is a device used for measuring or maintaining [orientation](/wiki/Orientation_(geometry) "Orientation (geometry)") and [angular velocity](/wiki/Angular_velocity "Angular velocity").[\[1\]](#cite_note-1)[\[2\]](#cite_note-2) It is a spinning wheel or disc in which the axis of rotation (spin axis) is free to assume any orientation by itself. When rotating, the orientation of this axis is unaffected by tilting or rotation of the mounting, according to the [conservation of angular momentum](/wiki/Angular_momentum#Conservation_of_angular_momentum "Angular momentum").

Gyroscopes based on other operating principles also exist, such as the microchip-packaged [MEMS gyroscopes](/wiki/Vibrating_structure_gyroscope#MEMS_gyroscopes "Vibrating structure gyroscope") found in electronic devices (sometimes called **gyrometers**), solid-state [ring lasers](/wiki/Ring_laser_gyroscope "Ring laser gyroscope"), [fibre optic gyroscopes](/wiki/Fibre_optic_gyroscope "Fibre optic gyroscope"), and the extremely sensitive [quantum gyroscope](/wiki/Quantum_gyroscope "Quantum gyroscope").[\[3\]](#cite_note-3)

Applications of gyroscopes include [inertial navigation systems](/wiki/Inertial_navigation_system "Inertial navigation system"), such as in the [Hubble Space Telescope](/wiki/Hubble_Space_Telescope "Hubble Space Telescope"), or inside the steel hull of a submerged submarine. Due to their precision, gyroscopes are also used in [gyrotheodolites](/wiki/Gyrotheodolite "Gyrotheodolite") to maintain direction in tunnel mining.[\[4\]](#cite_note-4) Gyroscopes can be used to construct [gyrocompasses](/wiki/Gyrocompass "Gyrocompass"), which complement or replace [magnetic compasses](/wiki/Magnetic_Compass "Magnetic Compass") (in ships, aircraft and spacecraft, vehicles in general), to assist in stability (bicycles, motorcycles, and ships) or be used as part of an [inertial guidance system](/wiki/Inertial_guidance_system "Inertial guidance system").

MEMS gyroscopes are popular in some consumer electronics, such as smartphones.

## Description and diagram

\[ [edit](/w/index.php?title=Gyroscope&action=edit&section=1 "Edit section: Description and diagram")\]

[![](//upload.wikimedia.org/wikipedia/commons/thumb/3/35/Gyroscope_wheel-text.png/200px-Gyroscope_wheel-text.png)](/wiki/File:Gyroscope_wheel-text.png) Diagram of a gyro wheel. Reaction arrows about the output axis (blue) correspond to forces applied about the input axis (green), and vice versa.

A gyroscope is an instrument, consisting of a wheel mounted into two or three [gimbals](/wiki/Gimbal "Gimbal") providing pivoted supports, for allowing the wheel to rotate about a single axis. A set of three gimbals, one mounted on the other with orthogonal pivot axes, may be used to allow a wheel mounted on the innermost gimbal to have an orientation remaining independent of the orientation, in space, of its support.

In the case of a gyroscope with two gimbals, the outer gimbal, which is the gyroscope frame, is mounted so as to pivot about an axis in its own plane determined by the support. This outer gimbal possesses one degree of rotational freedom and its axis possesses none. The second gimbal, inner gimbal, is mounted in the gyroscope frame (outer gimbal) so as to pivot about an axis in its own plane that is always perpendicular to the pivotal axis of the gyroscope frame (outer gimbal). This inner gimbal has two degrees of rotational freedom.

The axle of the spinning wheel (the rotor) defines the spin axis. The rotor is constrained to spin about an axis, which is always perpendicular to the axis of the inner gimbal. So the rotor possesses three degrees of rotational freedom and its axis possesses two.
The rotor responds to a force applied to the input axis by a reaction force to the output axis.

A gyroscope flywheel will roll or resist about the output axis depending upon whether the output gimbals are of a free or fixed configuration. An example of some free-output-gimbal devices is the [attitude control](/wiki/Spacecraft_attitude_control "Spacecraft attitude control") gyroscopes used to sense or measure the pitch, roll and yaw attitude angles in a spacecraft or aircraft.

[![](//upload.wikimedia.org/wikipedia/commons/thumb/2/26/Gyroscope_wheel_animation.gif/200px-Gyroscope_wheel_animation.gif)](/wiki/File:Gyroscope_wheel_animation.gif) Animation of a gyro wheel in action

The centre of gravity of the rotor can be in a fixed position. The rotor simultaneously spins about one axis and is capable of oscillating about the two other axes, and it is free to turn in any direction about the fixed point (except for its inherent resistance caused by rotor spin). Some gyroscopes have mechanical equivalents substituted for one or more of the elements. For example, the spinning rotor may be suspended in a fluid, instead of being mounted in gimbals. A [control moment gyroscope](/wiki/Control_moment_gyroscope "Control moment gyroscope") (CMG) is an example of a fixed-output-gimbal device that is used on spacecraft to hold or maintain a desired attitude angle or pointing direction using the gyroscopic resistance force.

In some special cases, the outer gimbal (or its equivalent) may be omitted so that the rotor has only two degrees of freedom. In other cases, the centre of gravity of the rotor may be offset from the axis of oscillation, and thus the centre of gravity of the rotor and the centre of suspension of the rotor may not coincide.

## History

\[ [edit](/w/index.php?title=Gyroscope&action=edit&section=2 "Edit section: History")\]

[![](//upload.wikimedia.org/wikipedia/commons/thumb/0/08/Foucault%27s_gyroscope.jpg/220px-Foucault%27s_gyroscope.jpg)](/wiki/File:Foucault%27s_gyroscope.jpg) Gyroscope designed by [Léon Foucault](/wiki/L%C3%A9on_Foucault "Léon Foucault") in 1852. Replica built by Dumoulin-Froment for the Exposition universelle in 1867. [National Conservatory of Arts and Crafts museum](/wiki/Conservatoire_national_des_arts_et_m%C3%A9tiers "Conservatoire national des arts et métiers"), Paris.

### Early similar devices

\[ [edit](/w/index.php?title=Gyroscope&action=edit&section=3 "Edit section: Early similar devices")\]

Essentially, a gyroscope is a [top](/wiki/Spinning_top "Spinning top") combined with a pair of [gimbals](/wiki/Gimbal "Gimbal"). Tops were invented in many different civilizations, including classical Greece, Rome, and China.[\[5\]](#cite_note-5) Most of these were not utilized as instruments.

The first known apparatus similar to a gyroscope (the "Whirling Speculum" or "Serson's Speculum") was invented by [John Serson](/wiki/John_Serson "John Serson") in 1743. It was used as a level, to locate the horizon in foggy or misty conditions.

The first instrument used more like an actual gyroscope was made by [Johann Bohnenberger](/wiki/Johann_Bohnenberger "Johann Bohnenberger") of Germany, who first wrote about it in 1817. At first he called it the "Machine".[\[6\]](#cite_note-6)[\[7\]](#cite_note-7)[\[8\]](#cite_note-8) Bohnenberger's machine was based on a rotating massive sphere.[\[9\]](#cite_note-9) In 1832, American Walter R. Johnson developed a similar device that was based on a rotating disc.[\[10\]](#cite_note-10)[\[11\]](#cite_note-11) The French mathematician [Pierre-Simon Laplace](/wiki/Pierre-Simon_Laplace "Pierre-Simon Laplace"), working at the [École Polytechnique](/wiki/%C3%89cole_Polytechnique "École Polytechnique") in Paris, recommended the machine for use as a teaching aid, and thus it came to the attention of [Léon Foucault](/wiki/L%C3%A9on_Foucault "Léon Foucault").[\[12\]](#cite_note-12)

### Foucault's gyroscope

\[ [edit](/w/index.php?title=Gyroscope&action=edit&section=4 "Edit section: Foucault's gyroscope")\]

Main article: [Foucault gyroscope](/wiki/Foucault_gyroscope "Foucault gyroscope")

In 1852, Foucault used it in an experiment demonstrating the rotation of the Earth.[\[13\]](#cite_note-13)[\[14\]](#cite_note-14)

It was Foucault who gave the device its modern name, in an experiment to see (Greek _skopeein_, to see) the Earth's rotation (Greek _gyros_, circle or rotation),[\[15\]](#cite_note-OED-15)[\[16\]](#cite_note-16) which was visible in the 8 to 10 minutes before friction slowed the spinning rotor.

### Commercialization

\[ [edit](/w/index.php?title=Gyroscope&action=edit&section=5 "Edit section: Commercialization")\]

In the 1860s, the advent of electric motors made it possible for a gyroscope to spin indefinitely; this led to the first prototype [heading indicators](/wiki/Heading_indicator "Heading indicator"), and a rather more complicated device, the [gyrocompass](/wiki/Gyrocompass "Gyrocompass"). The first functional gyrocompass was patented in 1904 by German inventor [Hermann Anschütz-Kaempfe](/wiki/Hermann_Ansch%C3%BCtz-Kaempfe "Hermann Anschütz-Kaempfe").[\[17\]](#cite_note-17) American [Elmer Sperry](/wiki/Elmer_Sperry "Elmer Sperry") followed with his own design later that year, and other nations soon realized the military importance of the invention—in an age in which naval prowess was the most significant measure of military power—and created their own gyroscope industries. The [Sperry Gyroscope Company](/wiki/Sperry_Gyroscope_Company "Sperry Gyroscope Company") quickly expanded to provide aircraft and naval stabilizers as well, and other gyroscope developers followed suit.[\[18\]](#cite_note-18)\[ _[full citation needed](/wiki/Wikipedia:Citing_sources#What_information_to_include "Wikipedia:Citing sources")_\]

Circa 1911 the L.T. Hurst Mfg Co of Indianapolis started producing the "Hurst gyroscope" a toy gyroscope with a pull string and pedestal. Manufacture was at some point switched to Chandler Mfg Co (still branded Hurst). The product later gets renamed to a “Chandler gyroscope”, presumably because Chandler Mfg Co. took over rights to the gyroscope. Chandler continued to produce the toy until the company was purchased by TEDCO Inc. in 1982. The gyroscope is still produced by TEDCO today.[\[19\]](#cite_note-19)[\[20\]](#cite_note-20)

In the first several decades of the 20th century, other inventors attempted (unsuccessfully) to use gyroscopes as the basis for early [black box](/wiki/Flight_recorder "Flight recorder") navigational systems by creating a stable platform from which accurate acceleration measurements could be performed (in order to bypass the need for star sightings to calculate position). Similar principles were later employed in the development of [inertial navigation systems](/wiki/Inertial_navigation_system "Inertial navigation system") for [ballistic missiles](/wiki/Ballistic_missile "Ballistic missile").[\[21\]](#cite_note-21)\[ _[full citation needed](/wiki/Wikipedia:Citing_sources#What_information_to_include "Wikipedia:Citing sources")_\]

During World War II, the gyroscope became the prime component for aircraft and anti-aircraft gun sights.[\[22\]](#cite_note-22) After the war, the race to miniaturize gyroscopes for guided missiles and weapons navigation systems resulted in the development and manufacturing of so-called **midget gyroscopes** that weighed less than 3 ounces (85 g) and had a diameter of approximately 1 inch (2.5 cm). Some of these miniaturized gyroscopes could reach a speed of 24,000 revolutions per minute in less than 10 seconds.[\[23\]](#cite_note-23)

Gyroscopes continue to be an engineering challenge. For example, the axle bearings have to be extremely accurate. A small amount of friction is deliberately introduced to the bearings, since otherwise an accuracy of better than 10−7{\\displaystyle 10^{-7}}![{\displaystyle 10^{-7}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/60f7bc29238b21553311d8359274b4782ecb3f73) of an inch (2.5 nm) would be required.[\[24\]](#cite_note-FOOTNOTEFeynmanGottliebLeighton2013148–149-24)

Three-axis MEMS-based gyroscopes are also being used in portable electronic devices such as [tablets](/wiki/Tablet_(computer) "Tablet (computer)"),[\[25\]](#cite_note-25) [smartphones](/wiki/Smartphone "Smartphone"),[\[26\]](#cite_note-26) and [smartwatches](/wiki/Smartwatch "Smartwatch").[\[27\]](#cite_note-27) This adds to the 3-axis acceleration sensing ability available on previous generations of devices. Together these sensors provide 6 component motion sensing; accelerometers for X, Y, and Z movement, and gyroscopes for measuring the extent and rate of rotation in space (roll, pitch and yaw). Some devices[\[28\]](#cite_note-28)[\[29\]](#cite_note-29) additionally incorporate a [magnetometer](/wiki/Magnetometer "Magnetometer") to provide absolute angular measurements relative to the Earth's magnetic field. Newer [MEMS-based inertial measurement units](/wiki/Vibrating_structure_gyroscope#MEMS_gyroscopes "Vibrating structure gyroscope") incorporate up to all nine axes of sensing in a single integrated circuit package, providing inexpensive and widely available motion sensing.[\[30\]](#cite_note-30)

## Gyroscopic principles

\[ [edit](/w/index.php?title=Gyroscope&action=edit&section=6 "Edit section: Gyroscopic principles")\]

All spinning objects have gyroscopic properties. The main properties that an object can experience in any gyroscopic motion are [rigidity in space](/wiki/Axial_parallelism "Axial parallelism") and [precession](/wiki/Precession "Precession").

### Rigidity in space

\[ [edit](/w/index.php?title=Gyroscope&action=edit&section=7 "Edit section: Rigidity in space")\]

Main article: [Axial parallelism](/wiki/Axial_parallelism "Axial parallelism")

Rigidity in space describes the principle that a gyroscope remains in the fixed position on the plane in which it is spinning, unaffected by the Earth's rotation. For example, a bike wheel. Early forms of gyroscope (not then known by the name) were used to demonstrate the principle.[\[31\]](#cite_note-The_Encyclopaedia_Britannica:_A_Dictionary_of_Arts,_Sciences_and_General_Literature_1890_p._351-31)

### Precession

\[ [edit](/w/index.php?title=Gyroscope&action=edit&section=8 "Edit section: Precession")\]

Main article: [Axial precession](/wiki/Axial_precession "Axial precession")

A simple case of precession, also known as steady precession, can be described by the following relation to Moment:

∑Mx=−Iϕ′2sin⁡θcos⁡θ+Izϕ′sin⁡θ(ϕ′cos⁡θ+ψ′){\\displaystyle \\sum M\_{x}=-I{\\phi '}^{2}\\sin \\theta \\cos \\theta +I\_{z}\\phi '\\sin \\theta (\\phi '\\cos \\theta +\\psi ')}![{\displaystyle \sum M_{x}=-I{\phi '}^{2}\sin \theta \cos \theta +I_{z}\phi '\sin \theta (\phi '\cos \theta +\psi ')}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5acfb4559f7765ef59861007b135ac30f72b2b49)

where ϕ′{\\displaystyle \\phi '}![{\displaystyle \phi '}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ac5304c739c4deec1d259e3235a419e6177fe77a) represents precession, ψ′{\\displaystyle \\psi '}![{\displaystyle \psi '}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3e4792d3361b67c2f3eb7a3394932d28a6ef2e7b) is represented by spin, θ{\\displaystyle \\theta }![{\displaystyle \theta }](https://wikimedia.org/api/rest_v1/media/math/render/svg/6e5ab2664b422d53eb0c7df3b87e1360d75ad9af) is the nutation angle, and I{\\displaystyle I}![{\displaystyle I}](https://wikimedia.org/api/rest_v1/media/math/render/svg/535ea7fc4134a31cbe2251d9d3511374bc41be9f) represents inertia along its respective axis. This relation is only valid with the Moment along the Y and Z axes are equal to 0.

The equation can be further reduced noting that the angular velocity along the z-axis is equal to the sum of the Precession and the Spin: ωz=ϕ′cos⁡θ+ψ′{\\displaystyle \\omega \_{z}=\\phi '\\cos \\theta +\\psi '}![{\displaystyle \omega _{z}=\phi '\cos \theta +\psi '}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c8e9edc156619ab23b1242f99bba699d801920af), Where ωz{\\displaystyle \\omega \_{z}}![{\displaystyle \omega _{z}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e6664a519a737b4e06b4668df3e837d4e4986db1) represents the angular velocity along the z axis.

∑Mx=−Iψ′2sin⁡θcos⁡θ+Izψ′(sin⁡θ)ωz{\\displaystyle \\sum M\_{x}=-I{\\psi '}^{2}\\sin \\theta \\cos \\theta +I\_{z}\\psi '(\\sin \\theta )\\omega \_{z}}![{\displaystyle \sum M_{x}=-I{\psi '}^{2}\sin \theta \cos \theta +I_{z}\psi '(\sin \theta )\omega _{z}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f5e773abdf5fcff5bc6dacf92ab1b8d058dfc04d)

or

∑Mx=ψ′sin⁡θ(Izωz−Iψ′cos⁡θ){\\displaystyle \\sum M\_{x}=\\psi '\\sin \\theta (I\_{z}\\omega \_{z}-I\\psi '\\cos \\theta )}![{\displaystyle \sum M_{x}=\psi '\sin \theta (I_{z}\omega _{z}-I\psi '\cos \theta )}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d1fe9bd1b079c2d6c02d8f9f684bf95fc1b25092)[\[32\]](#cite_note-32)\[ _[full citation needed](/wiki/Wikipedia:Citing_sources#What_information_to_include "Wikipedia:Citing sources")_\]

Gyroscopic [precession](/wiki/Precession "Precession") is torque induced. It is the rate of change of the angular momentum that is produced by the applied torque. Precession produces counterintuitive dynamic results such as a [spinning top](/wiki/Top_(toy) "Top (toy)") not falling over. Precession is used in aerospace applications for sensing changes of attitude and direction.

## Contemporary uses

\[ [edit](/w/index.php?title=Gyroscope&action=edit&section=9 "Edit section: Contemporary uses")\]

### Steadicam

\[ [edit](/w/index.php?title=Gyroscope&action=edit&section=10 "Edit section: Steadicam")\]

Main article: [Steadicam](/wiki/Steadicam "Steadicam")

A [Steadicam](/wiki/Steadicam "Steadicam") rig was employed during the filming of the 1983 film _[Return of the Jedi](/wiki/Return_of_the_Jedi "Return of the Jedi")_, in conjunction with two gyroscopes for extra stabilization, to film the background plates for the [speeder bike](/wiki/Speeder_bike "Speeder bike") chase. Steadicam inventor [Garrett Brown](/wiki/Garrett_Brown "Garrett Brown") operated the shot, walking through a redwood forest, running the camera at one frame per second. When projected at 24 frames per second, it gave the impression of flying through the air at perilous speeds.[\[33\]](#cite_note-33)[\[34\]](#cite_note-EmpireOfDreams-34)

### Heading indicator

\[ [edit](/w/index.php?title=Gyroscope&action=edit&section=11 "Edit section: Heading indicator")\]

Main article: [Heading indicator](/wiki/Heading_indicator "Heading indicator")

The heading indicator or directional gyro has an axis of rotation that is set horizontally, pointing north. Unlike a magnetic compass, it does not seek north. When being used in an airplane, for example, it will slowly drift away from north and will need to be reoriented periodically, using a magnetic compass as a reference.[\[35\]](#cite_note-FOOTNOTEFeynmanGottliebLeighton2013115–135-35)

### Gyrocompass

\[ [edit](/w/index.php?title=Gyroscope&action=edit&section=12 "Edit section: Gyrocompass")\]

Main article: [Gyrocompass](/wiki/Gyrocompass "Gyrocompass")

Unlike a directional gyro or heading indicator, a gyrocompass seeks north. It detects the rotation of the Earth about its axis and seeks the _true_ north, rather than the _magnetic_ north. Gyrocompasses usually have built-in damping to prevent overshoot when re-calibrating from sudden movement.

### Accelerometer

\[ [edit](/w/index.php?title=Gyroscope&action=edit&section=13 "Edit section: Accelerometer")\]

Main article: [Accelerometer](/wiki/Accelerometer "Accelerometer")

By determining an object's acceleration and integrating over time, the velocity of the object can be calculated. Integrating again, position can be determined. The simplest accelerometer is a weight that is free to move horizontally, which is attached to a spring and a device to measure the tension in the spring. This can be improved by introducing a counteracting force to push the weight back and to measure the force needed to prevent the weight from moving. A more complicated design consists of a gyroscope with a weight on one of the axes. The device will react to the force generated by the weight when it is accelerated, by integrating that force to produce a velocity.[\[36\]](#cite_note-FOOTNOTEFeynmanGottliebLeighton2013131–135-36)

## Variations

\[ [edit](/w/index.php?title=Gyroscope&action=edit&section=14 "Edit section: Variations")\]

### Gyrostat

\[ [edit](/w/index.php?title=Gyroscope&action=edit&section=15 "Edit section: Gyrostat")\]

A **gyrostat** consists of a massive flywheel concealed in a solid casing.[\[37\]](#cite_note-37)[\[38\]](#cite_note-38) 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](/wiki/Lord_Kelvin "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.[\[39\]](#cite_note-39) Kelvin[\[40\]](#cite_note-40) also made use of gyrostats to develop mechanical theories of the elasticity of matter and of the ether.[\[41\]](#cite_note-41) In modern [continuum mechanics](/wiki/Continuum_mechanics "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](/wiki/Eug%C3%A8ne_Cosserat "Eugène Cosserat") and [François Cosserat](/wiki/Fran%C3%A7ois_Cosserat "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.[\[42\]](#cite_note-42)

In modern times, the gyrostat concept is used in the design of attitude control systems for orbiting spacecraft and satellites.[\[43\]](#cite_note-43) For instance, the Mir space station had three pairs of internally mounted flywheels known as _gyrodynes_ or _control moment gyros_.[\[44\]](#cite_note-44)

In physics, there are several systems whose dynamical equations resemble the equations of motion of a gyrostat.[\[45\]](#cite_note-45) Examples include a solid body with a cavity filled with an inviscid, incompressible, homogeneous liquid,[\[46\]](#cite_note-46) the static equilibrium configuration of a stressed elastic rod in [elastica theory](/wiki/Elastica_theory "Elastica theory"),[\[47\]](#cite_note-47) the polarization dynamics of a light pulse propagating through a nonlinear medium,[\[48\]](#cite_note-48) the [Lorenz system](/wiki/Lorenz_system "Lorenz system") in chaos theory,[\[49\]](#cite_note-49) and the motion of an ion in a [Penning trap](/wiki/Penning_trap "Penning trap") mass spectrometer.[\[50\]](#cite_note-50)

### MEMS gyroscope

\[ [edit](/w/index.php?title=Gyroscope&action=edit&section=16 "Edit section: MEMS gyroscope")\]

Main article: [Vibrating structure gyroscope](/wiki/Vibrating_structure_gyroscope "Vibrating structure gyroscope")

A [microelectromechanical systems](/wiki/Microelectromechanical_systems "Microelectromechanical systems") (MEMS) gyroscope is a miniaturized gyroscope found in electronic devices. It takes the idea of the [Foucault pendulum](/wiki/Foucault_pendulum "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.[\[51\]](#cite_note-51)

### HRG

\[ [edit](/w/index.php?title=Gyroscope&action=edit&section=17 "Edit section: HRG")\]

The [hemispherical resonator gyroscope](/wiki/Hemispherical_resonator_gyroscope "Hemispherical resonator gyroscope") (HRG), also called a wine-glass gyroscope[\[52\]](#cite_note-52) 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.[\[53\]](#cite_note-53)

### VSG or CVG

\[ [edit](/w/index.php?title=Gyroscope&action=edit&section=18 "Edit section: VSG or CVG")\]

A [vibrating structure gyroscope](/wiki/Vibrating_structure_gyroscope "Vibrating structure gyroscope") (VSG), also called a Coriolis vibratory gyroscope (CVG),[\[54\]](#cite_note-54) 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.[\[55\]](#cite_note-55)

High quality [wine-glass resonators](/wiki/Vibrating_structure_gyroscope#Wine_glass_resonator "Vibrating structure gyroscope") are used for precise sensors like HRG.[\[56\]](#cite_note-56)

### DTG

\[ [edit](/w/index.php?title=Gyroscope&action=edit&section=19 "Edit section: DTG")\]

A dynamically tuned gyroscope (DTG) is a rotor suspended by a universal joint with flexure pivots.[\[57\]](#cite_note-57) 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

\[ [edit](/w/index.php?title=Gyroscope&action=edit&section=20 "Edit section: Ring laser gyroscope")\]

Main article: [Ring laser gyroscope](/wiki/Ring_laser_gyroscope "Ring laser gyroscope")

A [ring laser gyroscope](/wiki/Ring_laser_gyroscope "Ring laser gyroscope") relies on the [Sagnac effect](/wiki/Sagnac_effect "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](/wiki/Boeing_757 "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](/wiki/Honeywell "Honeywell") and [Boeing](/wiki/Boeing "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](/wiki/White_noise "White noise") to the vibration. The material of the block was also changed from quartz to a new glass ceramic [Cer-Vit](/wiki/Cer-Vit "Cer-Vit"), made by [Owens Corning](/wiki/Owens_Corning "Owens Corning"), because of helium leaks.[\[58\]](#cite_note-58)

### Fiber optic gyroscope

\[ [edit](/w/index.php?title=Gyroscope&action=edit&section=21 "Edit section: Fiber optic gyroscope")\]

Main article: [Fibre optic gyroscope](/wiki/Fibre_optic_gyroscope "Fibre optic gyroscope")

A [fiber optic gyroscope](/wiki/Fiber_optic_gyroscope "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](/wiki/Fiber_optic "Fiber optic") cable as long as 5 km. Like the [ring laser gyroscope](/wiki/Ring_laser_gyroscope "Ring laser gyroscope"), it makes use of the [Sagnac effect](/wiki/Sagnac_effect "Sagnac effect").[\[59\]](#cite_note-59)

### London moment

\[ [edit](/w/index.php?title=Gyroscope&action=edit&section=22 "Edit section: London moment")\]

A [London moment](/wiki/London_moment "London moment") gyroscope relies on the quantum-mechanical phenomenon, whereby a spinning [superconductor](/wiki/Superconductor "Superconductor") generates a [magnetic field](/wiki/Magnetic_field "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 [interpolated](/wiki/Interpolation "Interpolation") 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](/wiki/Gravity_Probe_B "Gravity Probe B") experiment measured changes in gyroscope spin axis orientation to better than 0.5 [milliarcseconds](/wiki/Minute_of_arc "Minute of arc") (1.4×10−7 degrees, or about 2.4×10−9 radians) over a one-year period.[\[60\]](#cite_note-60) This is equivalent to an [angular separation](/wiki/Angular_separation "Angular separation") the width of a human hair viewed from 32 kilometers (20 mi) away.[\[61\]](#cite_note-61)

The GP-B gyro consists of a nearly-perfect spherical [rotating mass](/wiki/Moment_of_inertia#Rotational_symmetry "Moment of inertia") made of [fused quartz](/wiki/Fused_quartz "Fused quartz"), which provides a [dielectric](/wiki/Dielectric "Dielectric") support for a thin layer of [niobium](/wiki/Niobium "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 [RPM](/wiki/Revolutions_per_minute "Revolutions per minute"), 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](/wiki/Rotational_symmetry "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.[\[62\]](#cite_note-62)

A sensitive [DC SQUID](/wiki/SQUID#DC_SQUID "SQUID") that can discriminate changes as small as one quantum, or about 2 ×10−15 [Wb](/wiki/Weber_(unit) "Weber (unit)"), is used to monitor the gyroscope. A [precession](/wiki/Precession "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.[\[63\]](#cite_note-63)[\[64\]](#cite_note-64)

## Other examples

\[ [edit](/w/index.php?title=Gyroscope&action=edit&section=23 "Edit section: Other examples")\]

### Helicopters

\[ [edit](/w/index.php?title=Gyroscope&action=edit&section=24 "Edit section: Helicopters")\]

Main article: [Helicopter](/wiki/Helicopter "Helicopter")

The main rotor of a helicopter acts like a gyroscope. Its motion is influenced by the principle of gyroscopic precession which is the concept that a force applied to a spinning object will have a maximum reaction approximately 90 degrees later. The reaction may differ from 90 degrees when other stronger forces are in play.[\[65\]](#cite_note-65) To change direction, helicopters must adjust the pitch angle and the angle of attack.[\[66\]](#cite_note-66)

### Gyro X

\[ [edit](/w/index.php?title=Gyroscope&action=edit&section=25 "Edit section: Gyro X")\]

Gyro X prototype vehicle created by Alex Tremulis and Thomas Summers in 1967. The car utilized gyroscopic precession to drive on two wheels. An assembly consisting of a flywheel mounted in a gimbal housing under the hood of the vehicle acted as a large gyroscope. The flywheel was rotated by hydraulic pumps creating a gyroscopic effect on the vehicle. A precessional ram was responsible for rotating the gyroscope to change the direction of the precessional force to counteract any forces causing the vehicle imbalance. The one-of-a-kind prototype is now at the Lane Motor Museum in Nashville, Tennessee.[\[67\]](#cite_note-67)

## Consumer electronics

\[ [edit](/w/index.php?title=Gyroscope&action=edit&section=26 "Edit section: Consumer electronics")\]

[![](//upload.wikimedia.org/wikipedia/commons/thumb/7/72/Digital_Compass_sensor_and_Arduino_Uno.jpg/220px-Digital_Compass_sensor_and_Arduino_Uno.jpg)](/wiki/File:Digital_Compass_sensor_and_Arduino_Uno.jpg) A digital gyroscope module connected to an [Arduino Uno](/wiki/Arduino_Uno "Arduino Uno") board

Main article: [Accelerometer § Consumer electronics](/wiki/Accelerometer#Consumer_electronics "Accelerometer")

In addition to being used in compasses, aircraft, computer pointing devices, etc., gyroscopes have been introduced into consumer electronics.

Since the gyroscope allows the calculation of orientation and rotation, designers have incorporated them into modern technology. The integration of the gyroscope has allowed for more accurate recognition of movement within a 3D space than the previous lone [accelerometer](/wiki/Accelerometer "Accelerometer") within a number of smartphones. Gyroscopes in consumer electronics are frequently combined with accelerometers for more robust direction- and motion-sensing. Examples of such applications include smartphones such as the [Samsung Galaxy Note 4](/wiki/Samsung_Galaxy_Note_4 "Samsung Galaxy Note 4"),[\[68\]](#cite_note-68) [HTC Titan](/wiki/HTC_Titan "HTC Titan"),[\[69\]](#cite_note-69) [Nexus 5](/wiki/Nexus_5 "Nexus 5"), [iPhone 5s](/wiki/IPhone_5s "IPhone 5s"),[\[70\]](#cite_note-70) [Nokia 808 PureView](/wiki/Nokia_808_PureView "Nokia 808 PureView")[\[71\]](#cite_note-71) and [Sony Xperia](/wiki/Sony_Xperia "Sony Xperia"), game console peripherals such as the [PlayStation 3 controller](/wiki/Sixaxis "Sixaxis") and the [Wii Remote](/wiki/Wii_Remote "Wii Remote"), and virtual reality headsets such as the [Oculus Rift](/wiki/Oculus_Rift_CV1 "Oculus Rift CV1").[\[72\]](#cite_note-72)

[Nintendo](/wiki/Nintendo "Nintendo") has integrated a gyroscope into the [Wii](/wiki/Wii "Wii") console's Wii Remote controller by an additional piece of hardware called " [Wii MotionPlus](/wiki/Wii_MotionPlus "Wii MotionPlus")".[\[73\]](#cite_note-73) It is also included in the [3DS](/wiki/Nintendo_3DS "Nintendo 3DS"), [Wii U](/wiki/Wii_U "Wii U") [GamePad](/wiki/Wii_U_GamePad "Wii U GamePad"), and [Nintendo Switch](/wiki/Nintendo_Switch "Nintendo Switch") [Joy-Con](/wiki/Joy-Con "Joy-Con") and [Pro](/wiki/Nintendo_Switch_Pro_Controller "Nintendo Switch Pro Controller") controllers, which detect movement when turning and shaking.

Cruise ships use gyroscopes to level motion-sensitive devices such as self-leveling pool tables.[\[74\]](#cite_note-74)

An electric powered flywheel gyroscope inserted in a bicycle wheel is sold as an alternative to training wheels.[\[75\]](#cite_note-75) Some features of Android phones like PhotoSphere or 360 Camera and to use VR gadget do not work without a gyroscope sensor in the phone.[\[76\]](#cite_note-76)

## See also

\[ [edit](/w/index.php?title=Gyroscope&action=edit&section=27 "Edit section: See also")\]

- [Aerotrim](/wiki/Aerotrim "Aerotrim")
- [Accelerometer](/wiki/Accelerometer "Accelerometer")
- [Anti-rolling gyro](/wiki/Anti-rolling_gyro "Anti-rolling gyro")
- [Attitude indicator](/wiki/Attitude_indicator "Attitude indicator")
- [Balancing machine](/wiki/Balancing_machine "Balancing machine")
- [Countersteering](/wiki/Countersteering "Countersteering")
- [Euler angles](/wiki/Euler_angles "Euler angles")
- [Eric Laithwaite](/wiki/Eric_Laithwaite "Eric Laithwaite")
- [Gyrocar](/wiki/Gyrocar "Gyrocar")
- [Gyro monorail](/wiki/Gyro_monorail "Gyro monorail")
- [Gyroscopic exercise tool](/wiki/Gyroscopic_exercise_tool "Gyroscopic exercise tool")
- [Inertial measurement unit](/wiki/Inertial_measurement_unit "Inertial measurement unit")
- [Magnetometer](/wiki/Magnetometer "Magnetometer")
- [Molecular gyroscope](/wiki/Molecular_gyroscope "Molecular gyroscope")
- [Reaction wheel](/wiki/Reaction_wheel "Reaction wheel")
- [Rifling](/wiki/Rifling "Rifling")
- [Rigid body dynamics](/wiki/Rigid_body_dynamics "Rigid body dynamics")
- [Turn and bank indicator](/wiki/Turn_and_bank_indicator "Turn and bank indicator")
- [Turn coordinator](/wiki/Turn_coordinator "Turn coordinator")
- [Stabilizer](/wiki/Stabilizer_(ship) "Stabilizer (ship)")

## Notes

\[ [edit](/w/index.php?title=Gyroscope&action=edit&section=28 "Edit section: Notes")\]

01. **[^](#cite_ref-1)**["Gyroscope"](https://web.archive.org/web/20150505003851/http://www.oxforddictionaries.com/definition/english/gyroscope). _Oxford Dictionaries_. Archived from [the original](http://www.oxforddictionaries.com/definition/english/gyroscope) on 5 May 2015. Retrieved 4 May 2015.
02. **[^](#cite_ref-2)**Kabai, Sándor (28 September 2007). ["Gyroscope"](https://demonstrations.wolfram.com/Gyroscope/). _[Wolfram Demonstrations Project](/wiki/Wolfram_Demonstrations_Project "Wolfram Demonstrations Project")_. [Wolfram](/wiki/Wolfram_Research "Wolfram Research"). [Archived](https://web.archive.org/web/20080430090205/http://demonstrations.wolfram.com/Gyroscope/) from the original on 30 April 2008.
03. **[^](#cite_ref-3)**Tao, W.; Liu, T.; Zheng, R.; Feng, H. (2012). ["Gait Analysis Using Wearable Sensors"](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3304165). _[Sensors](/wiki/Sensors_(journal) "Sensors (journal)")_. **12** (2). Basel, Switzerland: 2255–2283. [Bibcode](/wiki/Bibcode_(identifier) "Bibcode (identifier)"): [2012Senso..12.2255T](https://ui.adsabs.harvard.edu/abs/2012Senso..12.2255T). [doi](/wiki/Doi_(identifier) "Doi (identifier)"):[10.3390/s120202255](https://doi.org/10.3390%2Fs120202255). [PMC](/wiki/PMC_(identifier) "PMC (identifier)") [3304165](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3304165). [PMID](/wiki/PMID_(identifier) "PMID (identifier)") [22438763](https://pubmed.ncbi.nlm.nih.gov/22438763)..
04. **[^](#cite_ref-4)**["20 things you didn't know about tunnels"](http://discovermagazine.com/2009/may/20-things-you-didnt-know-about-tunnels). _[Discover](/wiki/Discover_(magazine) "Discover (magazine)")_. 29 April 2009. [Archived](https://web.archive.org/web/20090615212002/http://discovermagazine.com/2009/may/20-things-you-didnt-know-about-tunnels) from the original on 15 June 2009.
05. **[^](#cite_ref-5)**Range, Shannon K'doah; Mullins, Jennifer. ["Brief History of Gyroscopes"](https://web.archive.org/web/20150710113230/http://solarsystem.nasa.gov/scitech/display.cfm?ST_ID=327). Archived from [the original](http://solarsystem.nasa.gov/scitech/display.cfm?ST_ID=327) on 10 July 2015.
06. **[^](#cite_ref-6)**Johann G. F. Bohnenberger (1817) "Beschreibung einer Maschine zur Erläuterung der Gesetze der Umdrehung der Erde um ihre Axe, und der Veränderung der Lage der letzteren" (Description of a machine for the explanation of the laws of rotation of the Earth around its axis, and of the change of the orientation of the latter), [Tübinger Blätter für Naturwissenschaften und Arzneikunde](http://www.ion.org/museum/files/File_1.pdf) [Archived](https://web.archive.org/web/20110719070449/http://www.ion.org/museum/files/File_1.pdf) 19 July 2011 at the [Wayback Machine](/wiki/Wayback_Machine "Wayback Machine"), vol. 3, pages 72–83.
07. **[^](#cite_ref-7)**The French mathematician [Poisson](/wiki/Sim%C3%A9on_Denis_Poisson "Siméon Denis Poisson") mentions Bohnenberger's machine as early as 1813: Simeon-Denis Poisson (1813) "Mémoire sur un cas particulier du mouvement de rotation des corps pesans" \[Memoir on a special case of rotational movement of massive bodies\], _Journal de l'École Polytechnique_, vol. 9, pages 247–262. Available online at: [Ion.org](http://www.ion.org/museum/files/File_2.pdf) [Archived](https://web.archive.org/web/20110719070631/http://www.ion.org/museum/files/File_2.pdf) 19 July 2011 at the [Wayback Machine](/wiki/Wayback_Machine "Wayback Machine")
08. **[^](#cite_ref-8)**Wagner, Jörg F.; Trierenberg, Andor (2014), Stein, Erwin (ed.), ["The Machine of Bohnenberger"](https://doi.org/10.1007/978-3-642-39905-3_6), _The History of Theoretical, Material and Computational Mechanics – Mathematics Meets Mechanics and Engineering_, Lecture Notes in Applied Mathematics and Mechanics, Berlin, Heidelberg: Springer, pp. 81–100, [doi](/wiki/Doi_(identifier) "Doi (identifier)"): [10.1007/978-3-642-39905-3\_6](https://doi.org/10.1007%2F978-3-642-39905-3_6), [ISBN](/wiki/ISBN_(identifier) "ISBN (identifier)") [978-3-642-39905-3](/wiki/Special:BookSources/978-3-642-39905-3 "Special:BookSources/978-3-642-39905-3"), retrieved 20 February 2021
09. **[^](#cite_ref-9)**A photograph of Bohnenberger's instrument is available on-line here: [Ion.org](http://www.ion.org/museum/item_view.cfm?cid=5&scid=12&iid=24) [Archived](https://web.archive.org/web/20070928044532/http://www.ion.org/museum/item_view.cfm?cid=5&scid=12&iid=24) 28 September 2007 at the [Wayback Machine](/wiki/Wayback_Machine "Wayback Machine") ION Museum: The Machine of Bohnenberger.
10. **[^](#cite_ref-10)**Walter R. Johnson (January 1832). ["Description of an apparatus called the rotascope for exhibiting several phenomena and illustrating certain laws of rotary motion"](https://books.google.com/books?id=BjwPAAAAYAAJ&pg=PA266-IA2) [Archived](https://web.archive.org/web/20160819023327/https://books.google.com/books?id=BjwPAAAAYAAJ&pg=PA266-IA2) 19 August 2016 at the [Wayback Machine](/wiki/Wayback_Machine "Wayback Machine"), _The American Journal of Science and Art_, 1st series, vol. 21, no. 2, pages 265–280.
11. **[^](#cite_ref-11)**Drawings of Walter R. Johnson's gyroscope ("rotascope") were used to illustrate phenomena in the following lecture: E.S. Snell (1856) ["On planetary disturbances,"](https://books.google.com/books?id=fEyT4sTd7ZkC&pg=PA175) [Archived](https://web.archive.org/web/20160819023557/https://books.google.com/books?id=fEyT4sTd7ZkC&pg=PA175) 19 August 2016 at the [Wayback Machine](/wiki/Wayback_Machine "Wayback Machine") Board of Regents, _Tenth Annual Report of the Board of Regents of the Smithsonian Institution...._ (Washington, D.C.: Cornelius Wendell, 1856), pages 175–190.
12. **[^](#cite_ref-12)**["ION Museum: The Machine of Bohnenberger"](https://web.archive.org/web/20070928044532/http://www.ion.org/museum/item_view.cfm?cid=5&scid=12&iid=24). Archived from [the original](http://www.ion.org/museum/item_view.cfm?cid=5&scid=12&iid=24) on 28 September 2007. Retrieved 24 May 2007.
13. **[^](#cite_ref-13)**L. Foucault (1852) "Sur les phénomènes d’orientation des corps tournants entraînés par un axe fixe à la surface de la terre – Nouveaux signes sensibles du mouvement diurne" (On the phenomena of the orientation of rotating bodies carried along by an axis fixed to the surface of the earth – New perceptible signs of the daily movement), _Comptes rendus hebdomadaires des séances de l’Académie des Sciences (Paris)_, vol. 35, pages 424–427. Available on-line (in French): [Gallica.bnf.fr](http://gallica.bnf.fr/ark:/12148/bpt6k2992n/f428.image) [Archived](https://web.archive.org/web/20120716224438/http://gallica.bnf.fr/ark:/12148/bpt6k2992n/f428.image) 16 July 2012 at the [Wayback Machine](/wiki/Wayback_Machine "Wayback Machine")
14. **[^](#cite_ref-14)**Circa 1852, Friedrich Fessel, a German mechanic and former secondary school teacher, independently developed a gyroscope. See: **(1)** Julius Plücker (September 1853) "Über die Fessel'sche rotationsmachine", _Annalen der Physik_, vol. 166, no. 9, pages 174–177; **(2)** Julius Plücker (October 1853) "Noch ein wort über die Fessel'sche rotationsmachine", _Annalen der Physik_, vol. 166, no. 10, pages 348–351; **(3)** Charles Wheatstone (1864) ["On Fessel's gyroscope"](https://books.google.com/books?id=CtGEAAAAIAAJ&pg=RA1-PA307) [Archived](https://web.archive.org/web/20160819020402/https://books.google.com/books?id=CtGEAAAAIAAJ&pg=RA1-PA307) 19 August 2016 at the [Wayback Machine](/wiki/Wayback_Machine "Wayback Machine"), _Proceedings of the Royal Society of London_, vol. 7, pages 43–48.
15. **[^](#cite_ref-OED_15-0)**[_The Oxford English Dictionary_](https://www.oed.com/view/Entry/82917). Vol. VI (2nd ed.). 1989. p. 985. Retrieved 11 March 2023.
16. **[^](#cite_ref-16)**[Foucault, Léon](/wiki/L%C3%A9on_Foucault "Léon Foucault") (1852b). ["Mécanique: Sur les phénomènes d'orientation des corps tournants entraînés par un axe fixe à la surface de la Terre. Nouveaux signes sensibles du mouvement diurne"](https://books.google.com/books?id=KHJFAAAAcAAJ&pg=PA421). _Comptes rendus hebdomadaires des séances de l'Académie des Sciences_ (in French). **35** (Week of Monday 27 September 1852). Gauthier-Villars: 427.
17. **[^](#cite_ref-17)**Hermann Anschütz-Kaempfe and Friedrich von Schirach, ["Kreiselapparat"](http://v3.espacenet.com/publicationDetails/originalDocument?CC=DE&NR=182855C&KC=C&FT=D&date=&DB=&locale=) (Gyroscope) Deutsches Reichspatent no. 182855 (filed: 27 March 1904; issued: 2 April 1907).
18. **[^](#cite_ref-18)**MacKenzie, Donald. _Inventing Accuracy: A Historical Sociology of Nuclear Missile Guidance_. Cambridge: MIT Press, 1990. pp. 31–40. [ISBN](/wiki/ISBN_(identifier) "ISBN (identifier)") [0-262-13258-3](/wiki/Special:BookSources/0-262-13258-3 "Special:BookSources/0-262-13258-3")
19. **[^](#cite_ref-19)**Anon. ["TEDCO Toys – Cool company history, great science kits"](https://web.archive.org/web/20090309071225/https://blog.makezine.com/archive/2009/02/tedco_toys_cool_company_history_gre.html). _TEDCO Toys company website_. O'Reilly Media Inc. Archived from [the original](http://blog.makezine.com/archive/2009/02/tedco_toys_cool_company_history_gre.html) on 9 March 2009. Retrieved 23 December 2010.
20. **[^](#cite_ref-20)**["History of the Tedco Gyroscope"](https://www.gyroscope.com/history-of-the-tedco-gyroscope.asp). Brightfusion Ltd. Retrieved 10 May 2024.
21. **[^](#cite_ref-21)**MacKenzie, Donald. _Inventing Accuracy: A Historical Sociology of Nuclear Missile Guidance_. Cambridge: MIT Press, 1990. pp. 40–42. [ISBN](/wiki/ISBN_(identifier) "ISBN (identifier)") [0-262-13258-3](/wiki/Special:BookSources/0-262-13258-3 "Special:BookSources/0-262-13258-3")
22. **[^](#cite_ref-22)**[The Little Top That Aims a Gun](http://www.popsci.com/archive-viewer?id=PiEDAAAAMBAJ&pg=86&query=destroyer+escort) [Archived](https://web.archive.org/web/20110710151152/http://www.popsci.com/archive-viewer?id=PiEDAAAAMBAJ&pg=86&query=destroyer+escort) 10 July 2011 at the [Wayback Machine](/wiki/Wayback_Machine "Wayback Machine") by Gold Sanders, _[Popular Science](/wiki/Popular_Science "Popular Science")_, July 1945
23. **[^](#cite_ref-23)**Magazines, Hearst (1 March 1954). ["Popular Mechanics"](https://books.google.com/books?id=nNwDAAAAMBAJ&pg=PA148). Hearst Magazines. [Archived](https://web.archive.org/web/20170202032244/https://books.google.com/books?id=nNwDAAAAMBAJ&pg=PA148) from the original on 2 February 2017.
24. **[^](#cite_ref-FOOTNOTEFeynmanGottliebLeighton2013148–149_24-0)**[Feynman, Gottlieb & Leighton 2013](#CITEREFFeynmanGottliebLeighton2013), pp. 148–149.
25. **[^](#cite_ref-25)**["iPad – Compare Models"](https://www.apple.com/ipad/compare/). _Apple_. [Archived](https://web.archive.org/web/20121024015359/http://www.apple.com/ipad/compare/) from the original on 24 October 2012.
26. **[^](#cite_ref-26)**["iPhone 4 Gyroscope Teardown"](https://web.archive.org/web/20111124144402/http://www.ifixit.com/Teardown/iPhone-4-Gyroscope-Teardown/3156/1). 24 June 2010. Archived from [the original](http://www.ifixit.com/Teardown/iPhone-4-Gyroscope-Teardown/3156/1) on 24 November 2011. Retrieved 11 November 2011.
27. **[^](#cite_ref-27)**Kelon, Leo (9 September 2014). ["Smartwatches: Specs and reviews for the leading models"](https://www.bbc.com/news/technology-29107354). Technology. _[BBC News](/wiki/BBC_News "BBC News")_. [Archived](https://web.archive.org/web/20150828140736/http://www.bbc.com/news/technology-29107354) from the original on 28 August 2015.
28. **[^](#cite_ref-28)**["Best Android phones with Gyroscope and Accelerator"](https://aptgadget.com/android-phones-gyroscope-accelerator/). _AptGadget.com_. 24 June 2018. Retrieved 9 December 2020.
29. **[^](#cite_ref-29)**["Basic Sensors in iOS"](https://web.archive.org/web/20150723214608/https://www.safaribooksonline.com/library/view/basic-sensors-in/9781449309480/ch05.html). Archived from [the original](https://www.safaribooksonline.com/library/view/basic-sensors-in/9781449309480/ch05.html) on 23 July 2015. Retrieved 23 July 2015.
30. **[^](#cite_ref-30)**["LSM9DS0 iNEMO inertial module:3D accelerometer, 3D gyroscope, 3D magnetometer - STMicroelectronics"](https://web.archive.org/web/20150723233203/http://www.st.com/web/en/catalog/sense_power/FM89/SC1448/PF258556). Archived from [the original](http://www.st.com/web/en/catalog/sense_power/FM89/SC1448/PF258556) on 23 July 2015. Retrieved 23 July 2015.
31. **[^](#cite_ref-The_Encyclopaedia_Britannica:_A_Dictionary_of_Arts,_Sciences_and_General_Literature_1890_p._351_31-0)**[_The Encyclopaedia Britannica: A Dictionary of Arts, Sciences and General Literature_](https://books.google.com/books?id=wqwMAAAAYAAJ&pg=PA351). R.S. Peale. 1890. p. 351. Retrieved 2 December 2022. Under the title of precession instruments, various pieces of apparatus, involving the gyroscope principle, have been in use for a number of years for illustrating the precession of the equinoxes, and the parallelism of the earth's axis as it revolves round the sun.
32. **[^](#cite_ref-32)**Hibbeler, R.C (2016). _Engineering Mechanics: Dynamics Fourteenth Edition_. Hoboken, New Jersey: [Pearson Prentice Hall](/wiki/Pearson_Prentice_Hall "Pearson Prentice Hall"). pp. 627–629.
33. **[^](#cite_ref-33)**Brown, Garrett. "Return of the Jedi", _[American Cinematographer](/wiki/American_Cinematographer "American Cinematographer")_, June 1983.
34. **[^](#cite_ref-EmpireOfDreams_34-0)**_Empire of Dreams: The Story of the Star Wars Trilogy_ _Star Wars Trilogy_ Box Set DVD documentary, \[2004\]
35. **[^](#cite_ref-FOOTNOTEFeynmanGottliebLeighton2013115–135_35-0)**[Feynman, Gottlieb & Leighton 2013](#CITEREFFeynmanGottliebLeighton2013), pp. 115–135.
36. **[^](#cite_ref-FOOTNOTEFeynmanGottliebLeighton2013131–135_36-0)**[Feynman, Gottlieb & Leighton 2013](#CITEREFFeynmanGottliebLeighton2013), pp. 131–135.
37. **[^](#cite_ref-37)**William Thomson (1875). _Proc. London Math. Soc._, vol. 6, pages 190–194.
38. **[^](#cite_ref-38)**[Andrew Gray](/wiki/Andrew_Gray_(physicist) "Andrew Gray (physicist)") (1979). _A Treatise on Gyrostatics and Rotational Motion: Theory and Applications_ (Dover, New York)
39. **[^](#cite_ref-39)**![](//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Wikisource-logo.svg/12px-Wikisource-logo.svg.png)One or more of the preceding sentences incorporates text from a publication now in the [public domain](/wiki/Public_domain "Public domain"): [Greenhill, Alfred George](/wiki/Alfred_George_Greenhill "Alfred George Greenhill") (1911). " [Gyroscope and Gyrostat](https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Gyroscope_and_Gyrostat "s:1911 Encyclopædia Britannica/Gyroscope and Gyrostat")". In [Chisholm, Hugh](/wiki/Hugh_Chisholm "Hugh Chisholm") (ed.). _[Encyclopædia Britannica](/wiki/Encyclop%C3%A6dia_Britannica_Eleventh_Edition "Encyclopædia Britannica Eleventh Edition")_. Vol. 12 (11th ed.). Cambridge University Press. p. 769. This source has a detailed mathematical discussion of the theory of gyroscopy.
40. **[^](#cite_ref-40)**William Thomson, "Popular Lectures and Addresses", London: MacMillan, 1889, vol. 1.
41. **[^](#cite_ref-41)**Robert Kargon, Peter Achinstein, Baron William Thomson Kelvin: "Kelvin's Baltimore Lectures and Modern Theoretical Physics: Historical and Philosophical Perspectives" [The MIT Press](/wiki/The_MIT_Press "The MIT Press"), 1987, [ISBN](/wiki/ISBN_(identifier) "ISBN (identifier)") [978-0-262-11117-1](/wiki/Special:BookSources/978-0-262-11117-1 "Special:BookSources/978-0-262-11117-1")
42. **[^](#cite_ref-42)**E. Grekova, P. Zhilin (2001). _Journal of elasticity_, Springer, vol. 64, pages 29–70
43. **[^](#cite_ref-43)**Peter C. Hughes (2004). _Spacecraft Attitude Dynamics_ [ISBN](/wiki/ISBN_(identifier) "ISBN (identifier)") [0-486-43925-9](/wiki/Special:BookSources/0-486-43925-9 "Special:BookSources/0-486-43925-9")
44. **[^](#cite_ref-44)**D. M. Harland (1997) _The MIR Space Station_ (Wiley); D. M. Harland (2005) _The Story of Space Station MIR_ (Springer).
45. **[^](#cite_ref-45)**C. Tong (2009). _American Journal of Physics_ vol. 77, pages 526–537
46. **[^](#cite_ref-46)**N.N. Moiseyev and V.V. Rumyantsev (1968). _Dynamic Stability of Bodies Containing Fluid_ (Springer, New York)
47. **[^](#cite_ref-47)**[Joseph Larmor](/wiki/Joseph_Larmor "Joseph Larmor") (1884). _Proc. London Math. Soc._ vol. 15, pages 170–184
48. **[^](#cite_ref-48)**M.V. Tratnik and J.E. Sipe (1987). _Physical Review A_ vol. 35, pages 2965–2975
49. **[^](#cite_ref-49)**A.B. Gluhovsky (1982). _Soviet Physics Doklady_ vol. 27, pages 823–825
50. **[^](#cite_ref-50)**S. Eliseev et al. (2011). _Physical Review Letters_ vol. 107, paper 152501
51. **[^](#cite_ref-51)**Passaro, Vittorio M. N.; Cuccovillo, Antonello; Vaiani, Lorenzo; De Carlo, Martino; Campanella, Carlo Edoardo (7 October 2017). ["Gyroscope Technology and Applications: A Review in the Industrial Perspective"](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5677445). _Sensors (Basel, Switzerland)_. **17** (10): 2284. [Bibcode](/wiki/Bibcode_(identifier) "Bibcode (identifier)"): [2017Senso..17.2284P](https://ui.adsabs.harvard.edu/abs/2017Senso..17.2284P). [doi](/wiki/Doi_(identifier) "Doi (identifier)"):[10.3390/s17102284](https://doi.org/10.3390%2Fs17102284). [ISSN](/wiki/ISSN_(identifier) "ISSN (identifier)") [1424-8220](https://search.worldcat.org/issn/1424-8220). [PMC](/wiki/PMC_(identifier) "PMC (identifier)") [5677445](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5677445). [PMID](/wiki/PMID_(identifier) "PMID (identifier)") [28991175](https://pubmed.ncbi.nlm.nih.gov/28991175).
52. **[^](#cite_ref-52)**Grewal, Mohinder S. (2007). [_Global positioning systems, inertial navigation, and integration_](https://www.worldcat.org/oclc/663976587). Lawrence R. Weill, Angus P. Andrews (2nd ed.). Hoboken, N.J.: Wiley-Interscience. pp. 329–331. [ISBN](/wiki/ISBN_(identifier) "ISBN (identifier)") [978-1-61583-471-6](/wiki/Special:BookSources/978-1-61583-471-6 "Special:BookSources/978-1-61583-471-6"). [OCLC](/wiki/OCLC_(identifier) "OCLC (identifier)") [663976587](https://search.worldcat.org/oclc/663976587).
53. **[^](#cite_ref-53)**Carta, G.; Nieves, M. J.; Jones, I. S.; Movchan, N. V.; Movchan, A. B. (21 October 2019). ["Flexural vibration systems with gyroscopic spinners"](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6732376). _Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences_. **377** (2156): 20190154. [Bibcode](/wiki/Bibcode_(identifier) "Bibcode (identifier)"): [2019RSPTA.37790154C](https://ui.adsabs.harvard.edu/abs/2019RSPTA.37790154C). [doi](/wiki/Doi_(identifier) "Doi (identifier)"): [10.1098/rsta.2019.0154](https://doi.org/10.1098%2Frsta.2019.0154). [ISSN](/wiki/ISSN_(identifier) "ISSN (identifier)") [1471-2962](https://search.worldcat.org/issn/1471-2962). [PMC](/wiki/PMC_(identifier) "PMC (identifier)") [6732376](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6732376). [PMID](/wiki/PMID_(identifier) "PMID (identifier)") [31474205](https://pubmed.ncbi.nlm.nih.gov/31474205).
54. **[^](#cite_ref-54)**H. Sternberg; C. Schwalm (2007). ["Qualification Process for MEMS Gyroscopes for the Use in Navigation Systems"](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)(PDF). _International Society for Photogrammetry and Remote Sensing Proceedings_. Archived from [the original](http://www.isprs.org/proceedings/XXXVI/5-C55/www.cirgeo.unipd.it/cirgeo/convegni/mmt2007/proceedings/papers/sternberg_harald.pdf)(PDF) on 2 October 2011.
55. **[^](#cite_ref-55)**Ash, M E; Trainor, C V; Elliott, R D; Borenstein, J T; Kourepenis, A S; Ward, P A; Weinberg, M S (14–15 September 1999). ["Micromechanical inertial sensor development at Draper Laboratory with recent test results"](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). _Symposium Gyro Technology Proceedings_. Archived from [the original](http://md1.csa.com/partners/viewrecord.php?requester=gs&collection=TRD&recid=A0017841AH&q=coriolis+vibratory+gyroscope+CVG&uid=789572486&setcookie=yes) on 23 August 2012.
56. **[^](#cite_ref-56)**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](/wiki/ISBN_(identifier) "ISBN (identifier)") [978-976-0-25248-5](/wiki/Special:BookSources/978-976-0-25248-5 "Special:BookSources/978-976-0-25248-5") (2009)
57. **[^](#cite_ref-57)**David May (1999). Masten, Michael K; Stockum, Larry A (eds.). ["Modeling the dynamically tuned gyroscope in support of high-bandwidth capture loop design"](http://spiedl.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PSISDG003692000001000101000001&idtype=cvips&gifs=yes&ref=no). _Proc. SPIE_. Acquisition, Tracking, and Pointing XIII. **3692**: 101–111. [Bibcode](/wiki/Bibcode_(identifier) "Bibcode (identifier)"): [1999SPIE.3692..101M](https://ui.adsabs.harvard.edu/abs/1999SPIE.3692..101M). [doi](/wiki/Doi_(identifier) "Doi (identifier)"): [10.1117/12.352852](https://doi.org/10.1117%2F12.352852). [S2CID](/wiki/S2CID_(identifier) "S2CID (identifier)") [121290096](https://api.semanticscholar.org/CorpusID:121290096).\[ _[permanent dead link](/wiki/Wikipedia:Link_rot "Wikipedia:Link rot")_\]
58. **[^](#cite_ref-58)**Donald MacKenzie, _Knowing Machines: Essays in Technical Change_, MIT Press, 1996, Chapter 4: _From the Luminiferous Ether to the Boeing 757_
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60. **[^](#cite_ref-60)**[Einstein.stanford.edu](http://einstein.stanford.edu/content/fact_sheet/GPB_FactSheet-0405.pdf) [Archived](https://web.archive.org/web/20110514044333/http://einstein.stanford.edu/content/fact_sheet/GPB_FactSheet-0405.pdf) 14 May 2011 at the [Wayback Machine](/wiki/Wayback_Machine "Wayback Machine"). "The GP-B instrument is designed
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61. **[^](#cite_ref-61)**["Gravity Probe B – Extraordinary Technologies"](https://web.archive.org/web/20100527111732/http://history.msfc.nasa.gov/gravity_probe_b/GravityProbeB_20050400.pdf)(PDF). Archived from [the original](http://history.msfc.nasa.gov/gravity_probe_b/GravityProbeB_20050400.pdf)(PDF) on 27 May 2010. Retrieved 18 January 2011.
62. **[^](#cite_ref-62)**["Gravity Probe B – Extraordinary Technologies"](https://web.archive.org/web/20110514043657/http://einstein.stanford.edu/TECH/technology1.html#gyros). _Einstein.stanford.edu_. Archived from [the original](http://einstein.stanford.edu/TECH/technology1.html#gyros) on 14 May 2011. Retrieved 5 November 2017.
63. **[^](#cite_ref-63)**Kobayashi, Takeshi; Hayakawa, Hisao; Tonouchi, Masayoshi (8 December 2003). [_Vortex Electronics and SQUIDs_](https://books.google.com/books?id=5mPeUu1i5R8C&q=dc+squid+reduce+lorentz+force&pg=PA44). Springer. pp. 44–45. [ISBN](/wiki/ISBN_(identifier) "ISBN (identifier)") [9783540402312](/wiki/Special:BookSources/9783540402312 "Special:BookSources/9783540402312"). [Archived](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) from the original on 4 September 2015.
64. **[^](#cite_ref-64)**["DC electrostatic gyro suspension system for the Gravity Probe B experiment"](https://www.researchgate.net/publication/234292394). _ResearchGate_. [Archived](https://web.archive.org/web/20150705144927/http://www.researchgate.net/publication/234292394_DC_electrostatic_gyro_suspension_system_for_the_Gravity_Probe_B_experiment) from the original on 5 July 2015.
65. **[^](#cite_ref-65)**["Learning Center Courses Content - FAA - FAASTeam - FAASafety.gov"](https://www.faasafety.gov/gslac/alc/course_content_popup.aspx?cID=104&sID=449). _Faasafety.gov_. Retrieved 23 April 2021.
66. **[^](#cite_ref-66)**["Gyroscopic Precession"](https://blog.aopa.org/aopa/2012/01/29/gyroscopic-precession/). _Blog.aopa.org_. 11 October 2020. Retrieved 23 April 2021.
67. **[^](#cite_ref-67)**Museum, Lane Motor. ["Gyro-X-1967"](https://www.lanemotormuseum.org/collection/cars/item/gyro-x-1967). _Lane Motor Museum_. Retrieved 23 April 2021.
68. **[^](#cite_ref-68)**["Samsung Galaxy and Gear – The Official Samsung Galaxy Site"](http://www.samsung.com/global/microsite/galaxynote4/note4_specs.html). _The Official Samsung Galaxy Site_. [Archived](https://web.archive.org/web/20141216101103/http://www.samsung.com/global/microsite/galaxynote4/note4_specs.html) from the original on 16 December 2014.
69. **[^](#cite_ref-69)**["HTC Titan Specifications and Features – Techstic"](https://web.archive.org/web/20121003033741/http://techstic.com/2011/10/htc-titan-specifications-and-features.html). 18 October 2011. Archived from [the original](http://techstic.com/2011/10/htc-titan-specifications-and-features.html) on 3 October 2012. Retrieved 6 May 2012.
70. **[^](#cite_ref-70)**["Nexus 5 vs iPhone 5s: Head-to-head – SiliconANGLE"](https://web.archive.org/web/20131213200443/http://siliconangle.com/blog/2013/11/01/nexus-5-vs-iphone-5s-head-to-head/). _Siliconangle.com_. 1 November 2013. Archived from [the original](http://siliconangle.com/blog/2013/11/01/nexus-5-vs-iphone-5s-head-to-head/) on 13 December 2013. Retrieved 5 November 2017.
71. **[^](#cite_ref-71)**["Nokia 808 PureView – Full phone specifications"](http://www.gsmarena.com/nokia_808_pureview-4577.php). _Gsmarena.com_. [Archived](https://web.archive.org/web/20120320160642/http://www.gsmarena.com/nokia_808_pureview-4577.php) from the original on 20 March 2012.
72. **[^](#cite_ref-72)**["Blog – Building a Sensor for Low Latency VR"](https://web.archive.org/web/20150308221700/https://www.oculus.com/blog/building-a-sensor-for-low-latency-vr/). _Oculus.com_. Archived from [the original](https://www.oculus.com/blog/building-a-sensor-for-low-latency-vr/) on 8 March 2015. Retrieved 5 November 2017.
73. **[^](#cite_ref-73)**Frank Caron (Aug 2008). [Of gyroscopes and gaming: the tech behind the Wii MotionPlus](https://arstechnica.com/gaming/news/2008/08/wii-motion-sensor.ars)
    The company has also used gyroscopes in the Nintendo Switch [Joy-Con](/wiki/Joy-Con "Joy-Con") controllers.
     [Archived](https://web.archive.org/web/20120415121613/http://arstechnica.com/gaming/news/2008/08/wii-motion-sensor.ars) 15 April 2012 at the [Wayback Machine](/wiki/Wayback_Machine "Wayback Machine"), ars technica
74. **[^](#cite_ref-74)**Sandler, Corey (2005). [_Econoguide Cruises 2006: Cruising the Caribbean, Hawaii, New England, Alaska, and Europe_](https://books.google.com/books?id=qqB7l5eoOKQC&q=self-leveling+pool+tables) (4th, illustrated ed.). Globe Pequot Press. p. 1. [ISBN](/wiki/ISBN_(identifier) "ISBN (identifier)") [978-0-7627-3871-7](/wiki/Special:BookSources/978-0-7627-3871-7 "Special:BookSources/978-0-7627-3871-7").
75. **[^](#cite_ref-75)**Adams, Paul (29 September 2009). ["Internal Gyroscope Is the Future of Training Wheels"](https://www.popsci.com/gear-amp-gadgets/article/2009-09/video-future-training-wheels). _Popular Science_. [Archived](https://web.archive.org/web/20160727105452/http://www.popsci.com/gear-amp-gadgets/article/2009-09/video-future-training-wheels) from the original on 27 July 2016. Retrieved 18 October 2017.
76. **[^](#cite_ref-76)**March 2020, Kevin Carbotte 18 (18 March 2020). ["HTC Vive Cosmos VR Headset Review: Solid Upgrade"](https://www.tomshardware.com/reviews/htc-vive-cosmos-vr-headset,6367.html). _Tom's Hardware_. Retrieved 2 April 2020.`{{cite web}}`: CS1 maint: numeric names: authors list ( [link](/wiki/Category:CS1_maint:_numeric_names:_authors_list "Category:CS1 maint: numeric names: authors list"))

## References

\[ [edit](/w/index.php?title=Gyroscope&action=edit&section=29 "Edit section: References")\]

- Feynman, Richard; Gottlieb, Michael; Leighton, Ralph (2013). _Feynman's Tips on Physics, A Problem-Solving Supplement to the Feynman Lectures on Physics_. Basic Books.

## Further reading

\[ [edit](/w/index.php?title=Gyroscope&action=edit&section=30 "Edit section: Further reading")\]

- [Felix Klein](/wiki/Felix_Klein "Felix Klein") and [Arnold Sommerfeld](/wiki/Arnold_Sommerfeld "Arnold Sommerfeld"), " _Über die Theorie des Kreisels_" (Tr., About the theory of the gyroscope). Leipzig, Berlin, B.G. Teubner, 1898–1914. 4 v. illus. 25 cm.
- Audin, M. _Spinning Tops: A Course on Integrable Systems_. New York: Cambridge University Press, 1996.
- Crabtree, H. "An Elementary Treatment of the Theory of Spinning Tops and Gyroscopic Motion". Longman, Green and C), 1909. Reprinted by Michigan Historical Reprint Series.
- Proceedings of Anniversary Workshop on Solid-State Gyroscopy, 19–21 May 2008. Yalta, Ukraine. Kyiv-Kharkiv. ATS of Ukraine, [ISBN](/wiki/ISBN_(identifier) "ISBN (identifier)") [978-976-0-25248-5](/wiki/Special:BookSources/978-976-0-25248-5 "Special:BookSources/978-976-0-25248-5") (2009)
- E. Leimanis (1965). _The General Problem of the Motion of Coupled Rigid Bodies about a Fixed Point_. (Springer, New York).
- Perry J. "Spinning Tops". London Society for Promoting Christian Knowledge, 1870. Reprinted by Project Gutemberg ebook, 2010.
- Walter Wrigley, Walter M. Hollister, and William G. Denhard (1969). _Gyroscopic Theory, Design, and Instrumentation._ (MIT Press, Cambridge, MA).
- Cooper, Donald & University of Western Australia. Dept. of Mechanical and Materials Engineering 1996, An investigation of the application of gyroscopic torque in the acceleration and retardation of rotating systems.

## External links

\[ [edit](/w/index.php?title=Gyroscope&action=edit&section=31 "Edit section: External links")\]

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- [The Royal Institution's 1974–75 Christmas Lecture](http://www.gyroscopes.org/1974lecture.asp) Professor Eric Laithwaite
- [One-Wheeled Robot-Gyrostat](http://demonstrations.wolfram.com/OneWheeledRobotGyrostat/) by Olga Kapustina and Yuri Martynenko [Wolfram Demonstrations Project](/wiki/Wolfram_Demonstrations_Project "Wolfram Demonstrations Project")
- Apostolyuk V. [Theory and Design of Micromechanical Vibratory Gyroscopes](http://www.apostolyuk.com/index.php/publications/12-journals/16-springer2006)

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