Note that the positive constant K « 1 for the periodic motion must still be determined. Now investigate the connection between the parameter K and the period of motion. It seems easier to determine the period of motion based on some physical considerations. In fact, for the SPS system to face the Sun in a circular orbit in the presence of a gravity-gradient torque with a half period r1( the condition is the complete elliptical integral of the first kind, and the initial condition with 0 = 0y = 0 at / = 0 is imposed. It is immediately seen that there is a specific 0„(O) or 0(0) from Eq. 6 along with the condition 0(0) = 0„(O) = Ofor which the periodic solutions exist. Specifying X permits the evaluation of k using an iterative method such as the Newton-Raphson technique. The complete trajectory for the problem can be obtained by integrating Eq. 9 which yields is the incomplete elliptical integral of the first kind. Note that the negative sign in Eq. 13 coincides with that of 0 which is also negative in this case. The attitude pointing error 0y in terms of 0 can thus be written as EQUILIBRIUM STATES IN THE NONCONSERVATIVE FIELD In Eq. 5, no frictional term is involved. Slightly more elaborate work is required
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