Foucaults pendulum

The functional principle of these kind of sensors is based on the effect that was discovered by G. H. Bryan in 1890 [8]. The sensor element of this gyroscope consists of a hollow, axial symmetrical resonator, such as a ring or a cylinder. It is possible to stimulate radial oscillations, which form a kind of standing wave on the wall of the cylinder. If the cylinder rotates around its axis, the nodes of the oscillation waves remain at rest, similar to Foucaults pendulum. 

Fig. 3.5. (a) Rotating system of coordinates, (b) Foucault s pendulum, (c) illustration of pendulum path. 

A and B are constants and they are independent of time. Bearing in mind that = X + iy, it is simple to find functions x t) and y t), which describe a motion of the pendulum on the earth s surface. In accordance with Equation (3.88) a solution is represented as a product of two functions. The first one characterizes a swinging of the pendulum with the angular velocity p, which depends only on the gravitational field and the length /, while the second is also a sinusoidal function and its period is defined by the frequency of the earth s rotation and the latitude of the point, (Foucault s pendulum). In order to understand the behavior of the pendulum at the beginning consider the simplest case when a rotation is absent, co — 0. Then, we have... 

Eco, Umberto. Foucault s pendulum. San Diego (CA) Harcourt Brace Jovanovich, 1989. 641p. ISBN 0151327653... 

The earth s rotation around its axis can be seen from the apparent motion of the stars. The rotation can also be observed by mechanical experiments carried out on the surface of the earth, that is, with the help of Foucault s pendulum, or by observing of the motion of a rapidly rotating gyroscope. It is important that the rotation of the earth can also be observed by closed optical experiments. 

The excitation can be realized by electrostatic, electromagnetic, or piezoelectric methods. The detection is carried out by capacitive, piezoelectric, or piezoresistive techniques. The principle of vibrating gyroscopes can be traced back to Foucault s pendulum in 1851. There are numerous design possibilities for the construction of vibrating gyroscopes [1-5, 9] Fig. 7.2.1 shows one principle. 

Foucault pondulum A simple pendulum in which a heavy bob attached to a long wire is firee to swing in any direction. As a result of the earth s rotation, the plane of the pendulum s swing slowly turns (at the poles of the earth it makes one complete revolution in 24 hours). It was devised by the French physi-... 

Foucault s pendulum (Leon Foucault) Foucault s pendulum proves that Earth rotates. 

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