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Gyrostat

A gyrostat consists of a massive flywheel concealed in a solid casing. 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. Kelvin also made use of gyrostats to develop mechanical theories of the elasticity of matter and of the ether. 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.

In modern times, the gyrostat concept is used in the design of attitude control systems for orbiting spacecraft and satellites. For instance, the Mir space station had three pairs of internally mounted flywheels known as gyrodynes or control moment gyros.

In physics, there are several systems whose dynamical equations resemble the equations of motion of a gyrostat. Examples include a solid body with a cavity filled with an inviscid, incompressible, homogeneous liquid, the static equilibrium configuration of a stressed elastic rod in elastica theory, the polarization dynamics of a light pulse propagating through a nonlinear medium, the Lorenz system in chaos theory, and the motion of an ion in a Penning trap mass spectrometer.