Shuttle-tethered subsatellite system stability with a flexible massive tether

The effect of the in-plane transverse vibrations of a massive, flexible tether on the stability of the Shuttle-tethered subsatellite system about the deployed local vertical orientation is examined analytically and numerically. Within the linear range, the out-of-orbit plane (roll) equation is decoupled from the in-plane swing and extension/ contraction modes and has the form of a Mathieu equation. An application of the Floquet theorem shows that parametric instability can result for specific ratios of the tether wave frequency to the orbital rate. In addition, a forced resonance can be further superimposed due to the rotating atmosphere, especially for high-inclination orbits. The divergent time constant can be as small as several orbits for short tether lengths where the subsatellite mass is much less than the tether mass.