Towards Stable Interstellar Flight: Levitation of a Laser-Propelled Sailcraft*

TL;DR

This paper investigates the dynamic stability of a laser-levitated sailcraft for interstellar travel, using Lyapunov and SOS methods to identify stability regions and key parameters, providing a foundation for experimental validation.

Contribution

It introduces a novel stability analysis framework for laser-levitated sails, combining Lyapunov theory and SOS programming to determine stability regions and influential parameters.

Findings

The stability region of the sail is quantified under transverse and angular perturbations.

Simulation results align with theoretical stability analysis.

Key sail parameters affecting stability are identified.

Abstract

Exploring and traveling to distant stars has long fascinated humanity but has been limited due to the vast distances. The Breakthrough Starshot Program aims at eliminating this limitation by traveling to Alpha Centauri, which is 4.37 light-years away. Thus, it is only possible if a vehicle travels at a substantial fraction of the speed of light. The Breakthrough Starshot Program initiatives to develop a proof-of-concept that is accelerating a sail to relativistic speeds using a laser beam aimed at the sail. At this high speed, while a stable beam riding is one of the crucial concerns of this concept, the dynamic stability analysis of a sail is hardly present in the previous literature. Furthermore, it is important to investigate the dynamic stability in the experiment before driving the sail to relativistic speeds. As a proof of concept, we study the dynamic stability of the sail levitated at a certain height by a laser beam. The sail's dynamics are modeled as a rigid body whose shape is parameterized by a sweep function. We estimate the region of attraction (ROA) for dynamic stability analysis using Lyapunov theory and Sum-of-square (SOS) programming. The ROA confirms how much a levitated sail can tolerate the transverse and angular perturbations. We also conclude on some of the important parameters of the sail that affects the dynamic stability. Simulation results validate our theoretical analysis.