Schuler Period in LEO Satellites

This paper generalizes and extends the concept of the Schuler oscillation that occurs in the theory of inertial navigation systems, allowing one to see how the Schuler phenomenon affects inertial navigation systems operating in space. We show why a low earth orbit satellite's orbital period is identical to the period of the Schuler pendulum, which is the period of the errors for terrestrial inertial navigation systems. We also show that the generalized form of the Schuler oscillation takes the same form as the Hill-Clohessy-Wiltshire equations for satellite relative motion and that the period of the out-of-plane motion in neighboring satellite relative trajectories is the same as the Schuler period. Finally, we describe how INS gyro drift manifests itself in different coordinate systems for the orbital case. These results may assist orbital flight dynamics and attitude control systems engineers in the design and analysis of INS-equipped spacecraft