Angular momentum gyroscope with

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.

The attitude determination and control system (ADCS) must maintain the proper angular orientation of the satelHte in its orbit in order to keep the antennas pointed to the Earth and the solar arrays aimed toward the sun (for example). The two prevalent stabhization methods are spin stabihzation and body stabhization. In the former, the sateUite body spins and the angular momentum maintains a gyroscopic stiffness. The latter uses momentum wheels to keep the spacecraft body orientation fixed. Components of this subsystem include the momentum wheels, torquers (which interact with the Earth s magnetic field), gyros, sun and Earth sensors, and thrusters to maintain orientation. 

This is exactly analogous to a gyroscope or top, spinning at an angle (0) with an angular momentum ( M ) and angular velocity (Rgure 2.11). Thus,... 

Figure 4-11 A gyroscope with the angular momentum of the flywheel, Lf, together with x, y, and z components of Lf, at a given instant.

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