Precession gyroscope

The measurement of the Lense-Thirring effect is the first scientific goal of the HYPER project (Fig. 3) and will be more detailed in this section. The Lense-Thirring effect consists of a precession of a local reference frame (realized by inertial gyroscopes) and a non-local one realized by pointing the direction of fixed stars. This Lense-Thirring precession is given by ... 

In addition to the whirling vibration due to an out-of-balance force, another type of motion can occur in a free-spindle machine. When the bowl or basket is tilted the spindle may move in a circle. This slow gyratory motion is known as precession , and is similar to the precession of a gyroscope. It is usually most pronounced at high speeds, above the critical speed. 

When exposed to a static magnetic field B0, a spinning nucleus behaves like a gyroscope in a gravitational field. As illustrated by Fig. 1.2, the spin axis - which coincides with the magnetic moment vector p - precesses about B0. The frequency of precession, v0, is known as the Larmor frequency of the observed nucleus. 

Another angular momentum mass flowmeter was attempted using the principle of a gyroscope. It consisted of a pipe shaped in the form of a circle formed in a plane perpendicular to the direction of the process flow. If this pipe is oscillated around one axis, a precession-type moment is produced about the axis perpendicular to it, which is proportional to mass flow. The gyroscopic mass flowmeter can handle slurries in medium pressure and temperature ranges, but its industrial use is very limited because of its high cost and inability to handle high flow rates. 

When immersed in a magnetic field, a nueleus will experience a twisting force, or torque, which tends to line the spin axis of the nucleus up with the field, the same effect that causes two bar magnets to stick to each other in opposed directions. Because the nucleus is spinnirig, however, it will precess like a spinning top or gyroscope. 

Gyration—Motion similar to that of a gyroscope the precession of rotation axis. 

We have abstracted so far from the so-called Thomas precession. This originates in the relativistic transformations which account for the fact that the electron is moving in a curved path around a fixed nucleus. If an axis of the gyroscope obeys an own dynamical precession with the Larmor angular velocity coL = (e/m)B, then the corrected precession in the inertial system associated with the fixed nucleus is (o = (oL + o>r, the Thomas precession being... 

In Chapter 5 we found that in quantum mechanics L lies on the surface of a cone. A c/flSJica/-mechanical treatment Halliday and Resnick, Sections 13-2 and 37-7) of the motion of L in an applied magnetic field shows that the field exerts a torque on m, causing L to revolve about the direction of B at a constant frequency given by mi B/27r L, while maintaining a constant angle with B. This gyroscopic motion is called precession. In quantum mechanics, a complete specification of L is impossible however, one finds that (L) processes about the field direction Dicke and Wittke, Section 12-3). 

Fig. 12.10. Classical and quantum tops in space, (a) The space is isotropic and therefore the classical top ftteserves its angular momentum i.e.. its axis does not move with respect to distant stars and the top rotates about its axis with a cxxistant speed. This behavior is used in the gyroscopes that help to orient a spaceship with respect to distant stars, (b) The same tc in a homogeneous vector field. The space is no longer isotropic, and therefore the total angular momentum is no longer preserved. The projection of the total momentum on the field direction is still preserved. This is achieved by the precession of the top axis about the direction of the field, (c) A quantum top i.e., an elementary particle with spin quantum number / = in the magnetic field. The projection /- of its spin I is quantized /- =mjH with mj = —, + and, therefore, we have two energy eigenstates that correspond to two precession cones, directed up and down.

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