A formation flying around a halo orbit is discussed in this paper. We aim to form a natural and closed formation flying around a halo orbit to reduce fuel consumption. A method to form a periodic orbit using a monodromy matrix derived by linearizing the equation of motion of spacecraft is proposed, where the complex eigenvalues of the monodromy matrix and their corresponding eigenvectors are used to form multiple orbiting formations. Using the proposed method, it is confirmed that the formation in which a chief moves around the halo orbit a certain number of times and a deputy returns to its same relative position can be constructed with almost zero velocity increment. We also discuss the design of formation trajectories when adding velocity increments. The validity of the proposed method is confirmed by numerical calculations.
Wake survey of vortices shed from two co-rotating vortex generators in boundary layer developed on a flat plate was performed in low-speed wind tunnel. The two vortex generators were arranged in lateral direction on the plate at 20 deg angle of attack and the spacing of the models was varied as the control parameter in order to assess the interference in the wake flow. Five-holes pitot tube was used to visualize the distributions of velocity vector, total pressure loss and vorticity in a measurement plane which was set at 10c downstream of the models, where $c$ was chord length of the vortex generator. Drag coefficient was also estimated by the wake measurement. It was shown that two vortices shed from the models existed respectively when the spacing was large. The strength of Vortex A was always superior to that of Vortex B. Where Vortex A was defined by the vortex that was located in the upwash region generated by the other vortex (i.e. Vortex B). Note the vortex B was located in the downwash region generated by the other vortex (Vortex A). As the spacing between those two vortices A and B was decreased, two vortices were gradually dissipated. However, dissipation was more significant on Vortex B. The two vortices subsequently merged into a single vortex.
This study proposes a new method for shape control of non-spinning solar sails, in which Shape Memory Alloy (SMA) wires are exploited. An SMA wire is one of soft actuators that contracts at temperatures above its design value. In the proposed framework, the whole shape of a solar sail membrane is deformed via the contraction of SMA wires distributed over the membrane. The deformation results in the change in solar radiation pressure (SRP) torque acting on the solar sail-craft, which is applicable to fuel-free attitude control. In this paper, we investigate the theory of shape control using SMA wires. It is shown that a membrane under shape control behaves similarly both in a ground experiment and in a finite element method (FEM) analysis, demonstrating the validity of numerical modeling. With this result, the performance of shape control for a large membrane in a space environment is simulated by another FEM analysis. Results demonstrate that the proposed method is capable of producing SRP torque at an effective level for attitude control.