The problem is solved for the one-degree-of-freedom case. This solution is then applied to the POP axis of the SPS under the assumption that the other two axes are held fixed by an active attitude control system. The problem is illustrated in Figure 2.4-12. The equation of motion is Note that the variable on the left hand side is the inertial angle of the vehicle, but the variable on the right hand side is the local vertical orientation. Tor a circular orbit Define a non-dimensional time as and the ratio of inertias as Note that the magnitude of a always lies between 0 and 1. Then equation 2.4-38 can be written as

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