Modeling and Stability of a Laser Beam-Driven Sail

Traveling to distant stars has long fascinated humanity, but vast distances limited space exploration to our solar system. The Breakthrough Starshot Program aims at eliminating this limitation by traveling to Alpha Centauri, which is 4.37 light-years away. The idea is to accelerate a sail to relativistic speeds using a laser beam aimed at the sail. Stable beam-riding requires dynamic stability analysis of the sail. Currently, sail dynamic stability is not well understood and there is no agreement on the proper shape of the beam-driven sail. Here we study dynamic stability of a beam-driven sail modeled as a rigid body whose shape is parameterized by a sweep function. We analyze the stability of the beam-driven sail using linear system theory and deduce some crucial parameters of the sail. We estimate the region of attraction (ROA) using Lyapunov theory and Sum-of-square (SOS) programming. Simulation results validate our theoretical analysis.