## Main Body

Fig. 18-24. Spring Libration Damper for a Gravity-Gradient Stabilized Spacecraft

Magnetically Anchored Eddy Current Damper. A damper such as that used by GEOS-3 consists of two concentric spheres which can move relative to each other and are separated by silicone oil to provide viscous damping. The inner sphere is attached to a magnet which aligns or anchors itself to the Earth's magnetic field vector. The outer sphere is attached to the spacecraft's boom and is made of pyrolitic graphite for diamagnetic centering of forces on the inner sphere and aluminum for energy dissipation through eddy currents. The damping torque N„ is where c is the damping constant and B is the direction pf the net magnetic field in the body coordinate system. If A is the attitude matrix, a the angular velocity of the satellite, and B7 the direction of the magnetic field in inertial space, then the above expression can be rewritten in the form

Because the eddy currents are generated by a strong permanent magnet, the damping is strong over a wide range of altitudes. After the spacecraft is in its equilibrium position, the magnet continues to track the Earth's magnetic field and thus creates a disturbance torque on the spacecraft. Under certain combinations of damping coefficient, orbital parameters and moments of inertia, the damper tends to move the spacecraft into a nonzero bias attitude. In such cases, a limit cycle exists because the gravity-gradient moment unloaded is equal to but out of phase with the momentum added due to the magnetic field.

Eddy Current Rods. Ferromagnetic rods which are coated with a conducting copper sheet and fixed along the principal axes of a spacecraft can be used for libration damping. As the spacecraft librates, eddy currents are generated in the rods because of the change in the geomagnetic field relative to the body coordinate system. The number of rods used does not create a proportional increase in the damping coefficient because the flux density is reduced in each rod. The instantaneous power dissipated is proportional to the square of the rate of change of the magnetic field vector along the longitudinal axis of a rod. Because the eddy currents are generated by the geomagnetic field, the damping produced is inversely proportional to the sixth power of the orbital radius and is not adequate at high altitudes.

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