## Simple Construction Long Life

The earliest duel-spin satellite (OSO) used a two-degree-of-freedom pendulum nutation damper which consisted of a brass ball mounted at the top of a flexible steel rod [Cloutier, 1975]. The damping was provided by immersing the ball in silicone. Currently, one-degree-of-freedeom nutation dampers, such as those described below, are preferred.

Mathematical techniques used to study passive nutation damping include the Energy Sink method used by Likins  and the Routh-Hurwitz stability method [Likins, 1967]. Nutational stability has been studied using Liapunov's second method by Pringle . If the satellite has many rotating components with many dampers, the resulting equations have periodically varying coefficients and stability can be studied using Floquet analysis [Meirovitch, 1970]; this approach has been used by Johnson .

Eddy Current Damper. In an eddy current damper, the energy dissipation required for nutation damping is provided by the motion of a conducting plate relative to a magnet. The energy dissipation rate per unit weight due to the generation of eddy currents in the conductor is much greater than that of fluid dampers.

A typical pendulum eddy current damper, such as that used by the SAS series, consists of a Ni/Pt torsion wire parallel to the spin axis. The wire carries a pendulous copper vane which oscillates between the poles of an electromagnet. The drag force is proportional to the relative velocity between the vane and the electromagnet If d and p are the thickness and resistivity of the vane, and B is the magnetic induction between the poles, then the damping constant, c, is given by [Haines and Leondes, 1973]

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