FuelOptimal Trajectories of Aeroassisted Orbital Transfer with Plane Change

The fueloptimal control problem arising in noncoplanar orbital transfer employing aeroassist technology is addressed. The mission involves the transfer from high Earth orbit to low Earth orbit with plane change. The complete maneuver consists of a deorbit impulse to inject a vehicle from a circular orbit to elliptic orbit for the atmospheric entry, a boost impulse at the exit from the atmosphere for the vehicle to attain a desired orbital altitude and finally a reorbit impulse to circularize the path of the vehicle. In order to minimize the total fuel consumption, a performance index is chosen as the sum of the deorbit, boost, and reorbit impulses. Application of optimization principles leads us to a nonlinear, two-point, boundary value problem, which is solved by using a multiple shooting method.