Solving the heliogyro’s inverse problem

A heliogyro is a solar sail concept that divides the solar sail membrane into a number of long, slender blades of film extended from a central hub, maintained in a flat state through spin-induced tension. The heliogyro can redirect and scale the solar radiation pressure (SRP) force and can achieve attitude control by twisting the blades, similar to a helicopter rotor. Different pitch profiles exist, including pitching the blades in a collective, cyclic or combined collective and cyclic manner. While the forward mapping, i.e., computing the SRP force and moment generated by the heliogyro for a given pitch profile, is straightforward, the inverse of the problem is much more complex. However, this inverse problem (finding the blades’ pitch that results in a desired SRP force and/or moment) is crucial for heliogyro mission design and operations. This paper therefore solves the inverse problem numerically: first, only for a desired SRP force or SRP moment and subsequently for the fully coupled inverse problem. The developed methods are subsequently applied to track a reference trajectory that corrects for injection errors into a solar sail Sun-Earth sub-L1 halo orbit. I. Introductio