NUMERICAL RESULTS ON THE GENERAL TIME-OPTIMAL REST-TO-REST THREE-AXIS REORIENTATION OF A RIGID SPACECRAFT

The time-optimal results to the rest-to-rest three-axis reorientation of a rigid spacecraft are presented here as an equidistant conic projection with respect to the eigenvector sphere for all possible rest-to-rest reorientation maneuvers of a given slew angle. The pseudospectral method is used to obtain the numerical results over a selection of azimuths and elevations within the first octant of the eigenvector sphere. The equidistant conic projection method used in cartography then translates the three dimensional eigenvector coordinates to a cone surface surrounding the eigenvector sphere. The result is the interpolated solution set to equally space polar coordinates on a flat quadrant, given a chosen slew angle and inertial assumptions. Additionally, the latitude-longitude representation is applied to the attitude history of the principle axes of rotation of the rigid spacecraft as a trajectory mapping method. All projections are applicable to spherically symmetric, cylindrically symmetric, and triaxial spacecraft, and case studies are presented for each. All presented methods may be applied to represent other cost functionals and constraints as well.