Minimum torque earth off-nadir pointing control of gravity gradient stabilized small satellites

Earth off nadir pointing technology can be used on a small satellite to provide larger nadir earth surface imaging coverage. In this paper, the satellite attitude dynamics equations including the gravity gradient torque and wheel motor torque are derived using Euler parameters. The necessary conditions for optimum solutions subject to the performance index are obtained via Pontryagin s principle. The resulting two point boundary value problem is solved numerically with an optimal slew illustrated by example.