Editing Gyroscope (section)

===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>