Astrodynamics Commons^™

Modal Control Of An Unstable Periodic Orbit, William Wiesel, William Shelton

Faculty Publications

We apply Floquet theory to the problem of designing a control system for a satellite in an unstable periodic orbit. Expansion about a periodic orbit produces a time periodic linear system, which is augmented by a time periodic control term. We show that this can be done such that a) the application of control produces only inertial accelerations, b) positive real Poincare exponents are shifted into the left half-plane, and c) the shift of the exponent is linear with control gain. We apply these developments to an unstable orbit near the Earth-Moon L₃ point perturbed by the Sun. Finally, …