Resumen de Analysis on reachable set for spacecraft relative motion under low-thrust
Hill’s equations describe the linearized relative motion of deputy spacecraft with respect to the chief spacecraft which moves around the Earth in a circular orbit. The reachable set is defined as the set of all possible final positions of the deputy spacecraft that can be reached by a control force under certain constraints. The computation of the reachable set has been a focus of recent study, and different numerical methods are proposed. In this article, we use rigorous mathematical methods to study the structure and properties of the reachable set under the energy-limited constraint. We give an analytical expression for the computation of reachable set by using the methods of Hilbert space theory. According to the obtained analytical expression, the shape, volume, surface area and other properties of the reachable set are studied. In the end, the conclusions are verified numerically.
