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Figure 7.4 (a) Roll, pitch, and yaw axes. The yaw axis is directed toward the earth s center, the pitch axis is normal to the orbital plane, and the roll axis is perpendicular to the other two. (b) RPY axes for the geostationary orbit. Here, the roll axis is tangential to the orbit and lies along the satellite velocity vector.
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The three axes which define a satellite s attitude are its roll, pitch, and yaw (RPY) axes. These are shown relative to the earth in Fig. 7.4. All three axes pass through the center of gravity of the satellite. For an equatorial orbit, movement of the satellite about the roll axis moves the antenna footprint north and south; movement about the pitch axis moves the footprint east and west; and movement about the yaw axis rotates the antenna footprint.
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7.3.1 Spinning satellite stabilization
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Spin stabilization may be achieved with cylindrical satellites. The satellite is constructed so that it is mechanically balanced about one particular axis and is then set spinning around this axis. For geostationary satellites, the spin axis is adjusted to be parallel to the N-S axis of the earth, as illustrated in Fig. 7.5. Spin rate is typically in the range of 50 to 100 rev/min. Spin is initiated during the launch phase by means of small gas jets. In the absence of disturbance torques, the spinning satellite would maintain its correct attitude relative to the earth. Disturbance torques are generated in a number of ways, both external and internal to the satellite. Solar radiation, gravitational gradients, and meteorite impacts are all examples of external forces which can give rise to disturbance torques. Motor-bearing friction and the movement of satellite elements such as the antennas also can give rise to disturbance torques. The
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Spin stabilization in the geostationary orbit. The spin axis lies along the pitch axis, parallel to the earth s N-S axis.
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overall effect is that the spin rate will decrease, and the direction of the angular spin axis will change. Impulse-type thrusters, or jets, can be used to increase the spin rate again and to shift the axis back to its correct N-S orientation. Nutation, which is a form of wobbling, can occur as a result of the disturbance torques and/or from misalignment or unbalance of the control jets. This nutation must be damped out by means of energy absorbers known as nutation dampers. Where an omnidirectional antenna is used (e.g., as shown for the INTELSAT I and II satellites in Fig. 1.1), the antenna, which points along the pitch axis, also rotates with the satellite. Where a directional antenna is used, which is more common for communications satellites, the antenna must be despun, giving rise to a dual-spin construction. An electric motor drive is used for despinning the antenna subsystem. Figure 7.6 shows the Hughes HS 376 satellite in more detail. The antenna subsystem consists of a parabolic reflector and feed horns mounted on the despun shelf, which also carries the communications repeaters (transponders). The antenna feeds can therefore be connected directly to the transponders without the need for radiofrequency (rf) rotary joints, while the complete platform is despun. Of course, control signals and power must be transferred to the despun section, and a mechanical bearing must be provided. The complete assembly for this is known as the bearing and power transfer assembly (BAPTA). Figure 7.7 shows a photograph of the internal structure of the HS 376. Certain dual-spin spacecraft obtain spin stabilization from a spinning flywheel rather than by spinning the satellite itself. These flywheels are termed momentum wheels, and their average momentum is referred to as momentum bias. Reaction wheels, described in the Sec. 7.3.2, operate at zero momentum bias. In the Intelsat series of satellites, the INTELSAT-VI series spacecraft are spin-stabilized, all the others being 3-axis stabilized (body stabilized) through the use of momentum wheels.
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